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Deck 4: Applications of the Derivative
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Question
In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island. A cable is to be laid connecting the relay station with the experimental station. 
If the cost of running the cable on land is $2.00/running foot and the cost of running the cable under water is $5.20/running foot, locate the point P that will result in a minimum cost (solve for x).
A)
B)
C) 
D) 
E) 
If the cost of running the cable on land is $2.00/running foot and the cost of running the cable under water is $5.20/running foot, locate the point P that will result in a minimum cost (solve for x).
A)
B)
C)
D)
E)
Question
In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island. A cable is to be laid connecting the relay station with the experimental station.
If the cost of running the cable on land is $2.40/running foot and the cost of running the cable under water is $3.00/running foot, locate the point P that will result in a minimum cost (solve for x).
x = __________ ft
If the cost of running the cable on land is $2.40/running foot and the cost of running the cable under water is $3.00/running foot, locate the point P that will result in a minimum cost (solve for x).
x = __________ ft
Question
The management of the UNICO department store has decided to enclose an 400ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing material. 
If the pine board fencing costs $8/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.
A)
B)
C) 
D) 
If the pine board fencing costs $8/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.
A)
B)
C)
D)
Question
For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of 26 in.3 and is constructed using the least amount of metal.
A)
B) 
C) 
D) 
A)
B)
C)
D)
Question
Question
Question
A Norman window has the shape of a rectangle surmounted by a semicircle (see the accompanying figure). If a Norman window is to have a perimeter of 25 ft, what should its dimensions be in order to allow the maximum amount of light through the window? 
A)
B)
C) 
D) 
A)
B)
C)
D)
Question
Question
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 8 in. long and 3 in. wide, find the dimensions of the box that will yield the maximum volume.
A)
B)
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
The figure depicts a racetrack with ends that are semicircular in shape. The length of the track is 
. 
Find r and lso that the area enclosed by the rectangular region of the racetrack is as large as possible.
A)
B)
C) 
D) 
. Find r and lso that the area enclosed by the rectangular region of the racetrack is as large as possible.
A)
B)
C)
D)
Question
Question
If an open box has a square base and a volume of 500 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.
A)
B)
C) 
D) 
A)
B)
C)
D)
Question
Question
What are the dimensions of a closed rectangular box that has a square cross section, a capacity of 127 in.3 and is constructed using the least amount of material?
A)
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?
A)
B)
C) 
D) 
A)
B)
C)
D)
Question
A rectangular box is to have a square base and a volume of 4 ft.3. If the material for the base costs 20 cent/square foot, the material for the sides costs 30 cent/square foot, and the material for the top costs 10 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost. 
A)
B) 
C) 
D) 
A)
B)
C)
D)
Question
Question
Question
A book designer has decided that the pages of a book should have 1 in.margins at the top and bottom and 
in.margins on the sides. She further stipulated that each page should have an area of 27 in.2 (see the figure). 
Determine the page dimensions that will result in the maximum printed area on the page, where
.
A)
B) 
C) 
D) 
in.margins on the sides. She further stipulated that each page should have an area of 27 in.2 (see the figure). Determine the page dimensions that will result in the maximum printed area on the page, where
.
A)
B)
C)
D)
Question
Question
A rectangular box is to have a square base and a volume of 24 ft.3. If the material for the base costs 20 cent/square foot, the material for the sides costs 10 cent/square foot, and the material for the top costs 40 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost.
Question
Question
If an open box has a square base and a volume of 864 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.
Question
Find the absolute maximum value and the absolute minimum value, if any, of the function. 
on 
A) Absolute maximum value:
; absolute minimum value: 
B) Absolute maximum value:
; absolute minimum value: 
C) Absolute maximum value:
; absolute minimum value: 
D) Absolute maximum value:
; absolute minimum value: 
E) Absolute maximum value:
; absolute minimum value: 
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) Absolute maximum value:
; absolute minimum value: E) Absolute maximum value:
; absolute minimum value: Question
The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river.
If fencing is not required along the river, what are the dimensions of the largest area that he can enclose?
What is this area?
If fencing is not required along the river, what are the dimensions of the largest area that he can enclose?
What is this area?
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
A) Absolute maximum value:
; absolute minimum value: none
B) Absolute maximum value: none; absolute minimum value: 0
C) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
A) Absolute maximum value:
; absolute minimum value: noneB) Absolute maximum value: none; absolute minimum value: 0
C) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
Question
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
on 
A) Absolute maximum value:
; absolute minimum value: 
B) Absolute maximum value:
; absolute minimum value: 
C) Absolute maximum value:
; absolute minimum value: 
D) No absolute extrema
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) No absolute extrema
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
on 
A) Absolute maximum value: 2; absolute minimum value:
B) Absolute maximum value: 3; absolute minimum value:
C) Absolute maximum value: 3; absolute minimum value:
D) No absolute extrema
on A) Absolute maximum value: 2; absolute minimum value:
B) Absolute maximum value: 3; absolute minimum value:
C) Absolute maximum value: 3; absolute minimum value:
D) No absolute extrema
Question
Question
Find the absolute maximum value and the absolute minimum value, if any, of the function. 
on 
A) Absolute maximum value: 0; absolute minimum value: - 48
B) Absolute maximum value: 9; absolute minimum value: - 48
C) Absolute maximum value: 5; absolute minimum value: - 4
D) Absolute maximum value: 4; absolute minimum value: - 5
E) Absolute maximum value: 9; absolute minimum value: 0
on A) Absolute maximum value: 0; absolute minimum value: - 48
B) Absolute maximum value: 9; absolute minimum value: - 48
C) Absolute maximum value: 5; absolute minimum value: - 4
D) Absolute maximum value: 4; absolute minimum value: - 5
E) Absolute maximum value: 9; absolute minimum value: 0
Question
You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. 
F defined on
A) Absolute maximum value: 0.3; absolute minimum value: -6
B) Absolute maximum value: 0.3; absolute minimum value: -2
C) Absolute maximum value: -2; absolute minimum value: -6
D) Absolute maximum value: 0.3; absolute minimum value: 0
F defined on
A) Absolute maximum value: 0.3; absolute minimum value: -6
B) Absolute maximum value: 0.3; absolute minimum value: -2
C) Absolute maximum value: -2; absolute minimum value: -6
D) Absolute maximum value: 0.3; absolute minimum value: 0
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
A) Absolute maximum value: 4; absolute minimum value: none
B) Absolute maximum value: 2; absolute minimum value: - 2
C) Absolute maximum value: 2; absolute minimum value: none
D) No absolute extrema
A) Absolute maximum value: 4; absolute minimum value: none
B) Absolute maximum value: 2; absolute minimum value: - 2
C) Absolute maximum value: 2; absolute minimum value: none
D) No absolute extrema
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
on 
A) Absolute maximum value: 75; absolute minimum value: - 134
B) Absolute maximum value: 26; absolute minimum value: - 134
C) Absolute maximum value: 26; absolute minimum value: - 6
D) Absolute maximum value: 75; absolute minimum value: - 6
E) No absolute extrema
on A) Absolute maximum value: 75; absolute minimum value: - 134
B) Absolute maximum value: 26; absolute minimum value: - 134
C) Absolute maximum value: 26; absolute minimum value: - 6
D) Absolute maximum value: 75; absolute minimum value: - 6
E) No absolute extrema
Question
A book designer has decided that the pages of a book should have 1 in. margins at the top and bottom and 
in. margins on the sides. She further stipulated that each page should have an area of 72 in.2 (see the figure).
Determine the page dimensions that will result in the maximum printed area on the page, where
.
in. margins on the sides. She further stipulated that each page should have an area of 72 in.2 (see the figure).
Determine the page dimensions that will result in the maximum printed area on the page, where
.
Question
What are the dimensions of a closed rectangular box that has a square cross section, a capacity of 127 in.3 and is constructed using the least amount of material? Round the answer to two decimal places.
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
on 
A) Absolute maximum value: none; absolute minimum value: 0
B) Absolute maximum value: 0; absolute minimum value: -8
C) Absolute maximum value: 8; absolute minimum value: 0
D) No absolute extrema
on A) Absolute maximum value: none; absolute minimum value: 0
B) Absolute maximum value: 0; absolute minimum value: -8
C) Absolute maximum value: 8; absolute minimum value: 0
D) No absolute extrema
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
A) Absolute maximum value:
; absolute minimum value: none
B) Absolute maximum value:
; absolute minimum value: none
C) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
A) Absolute maximum value:
; absolute minimum value: noneB) Absolute maximum value:
; absolute minimum value: noneC) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
Question
You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. 
f defined on 
A) Absolute maximum value: 13.0; absolute minimum value: 6.7
B) Absolute maximum value: none; absolute minimum value: none
C) Absolute maximum value: none; absolute minimum value: 6.7
D) Absolute maximum value: 13.0; absolute minimum value: none
f defined on A) Absolute maximum value: 13.0; absolute minimum value: 6.7
B) Absolute maximum value: none; absolute minimum value: none
C) Absolute maximum value: none; absolute minimum value: 6.7
D) Absolute maximum value: 13.0; absolute minimum value: none
Question
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 4 in. long and 4 in. wide, find the dimensions of the box that will yield the maximum volume.
Question
A manufacturer of tennis rackets finds that the total cost 
(in dollars) of manufacturing 
rackets/day is given by 
. Each racket can be sold at a price of 
dollars, where 
is related to 
by the demand equation 
. If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
A) 5,000 rackets/day
B) 4,000 rackets/day
C) 7,000 rackets/day
D) 6,000 rackets/day
(in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation . If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
A) 5,000 rackets/day
B) 4,000 rackets/day
C) 7,000 rackets/day
D) 6,000 rackets/day
Question
Suppose the quantity demanded per week of a certain dress is related to the unit price 
by the demand equation 
, where 
is in dollars and 
is the number of dresses made.
To maximize the revenue, how many dresses should be made and sold each week?
by the demand equation , where is in dollars and is the number of dresses made.To maximize the revenue, how many dresses should be made and sold each week?
Question
The number of major crimes committed in the city between 1997 and 2004 is approximated by the function 
where 
denotes the number of crimes committed in year 
( 
corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens with the help of the local police organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.
When was the growth in the crime rate maximal?
A) 2001
B) 2003
C) 2000
D) 2002
E) 1999
where denotes the number of crimes committed in year ( corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens with the help of the local police organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.When was the growth in the crime rate maximal?
A) 2001
B) 2003
C) 2000
D) 2002
E) 1999
Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
on 
A) Absolute maximum value:
; absolute minimum value: 
B) Absolute maximum value:
; absolute minimum value: 
C) Absolute maximum value:
; absolute minimum value: 
D) No absolute extrema
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) No absolute extrema
Question
The average speed of a vehicle on a stretch of a route between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function
, where 
is measured in miles per hour and 
is measured in hours, with 
corresponding to 6 A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
time = __________ A.M.
average speed = __________ mph
, where is measured in miles per hour and is measured in hours, with corresponding to 6 A.M.At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
time = __________ A.M.
average speed = __________ mph
Question
The average speed of a vehicle on a stretch of a route between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function 
, where 
is measured in miles per hour and 
is measured in hours, with 
corresponding to 6 A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
A) time = 7 A.M. ; average speed = 50 mph
B) time = 7 A.M. ; average speed = 30 mph
C) time = 7 A.M. ; average speed = 45 mph
D) time = 7 A.M. ; average speed = 40 mph
, where is measured in miles per hour and is measured in hours, with corresponding to 6 A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
A) time = 7 A.M. ; average speed = 50 mph
B) time = 7 A.M. ; average speed = 30 mph
C) time = 7 A.M. ; average speed = 45 mph
D) time = 7 A.M. ; average speed = 40 mph
Question
A stone is thrown straight up from the roof of a 90-ft building. The height (in feet) of the stone at any time t (in seconds), measured from the ground, is given by 
What is the maximum height the stone reaches?
A) 115 ft
B) 126 ft
C) 108 ft
D) 112 ft
What is the maximum height the stone reaches?
A) 115 ft
B) 126 ft
C) 108 ft
D) 112 ft
Question
If 
is defined on a closed interval 
, then 
has an absolute maximum value.
is defined on a closed interval , then has an absolute maximum value. Question
A manufacturer of tennis rackets finds that the total cost 
(in dollars) of manufacturing 
rackets/day is given by 
. Each racket can be sold at a price of 
dollars, where 
is related to 
by the demand equation 
.
If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
__________ rackets/day
(in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation .
If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
__________ rackets/day
Question
The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation 
, where 
is measured in dollars and 
is measured in units of a thousand.
To yield a maximum revenue, how many watches must be sold?
__________
, where is measured in dollars and is measured in units of a thousand.To yield a maximum revenue, how many watches must be sold?
__________ Question
Find the absolute maximum value and the absolute minimum value, if any, of the given function. 
on 
A) Absolute maximum value:
; absolute minimum value: 
B) Absolute maximum value:
; absolute minimum value: 
C) Absolute maximum value:
; absolute minimum value: 
D) No absolute extrema
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) No absolute extrema
Question
Suppose the total cost function for manufacturing a certain product is 
dollars, where 
represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.
__________ units
dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.__________ units
Question
The number of major crimes committed in the city of Bronxville between 1997 and 2004 is approximated by the function
where 
denotes the number of crimes committed in year 
( 
corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens of Bronxville, with the help of the local police, organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.
Show that the growth in the crime rate was maximal in 2002, giving credence to the claim that the Neighborhood Crime Watch program was working.
where denotes the number of crimes committed in year ( corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens of Bronxville, with the help of the local police, organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.Show that the growth in the crime rate was maximal in 2002, giving credence to the claim that the Neighborhood Crime Watch program was working.
Question
The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling 
units of its model M1 camera is 
.
To maximize its profits, how many cameras should Cannon produce each month?
__________ cameras
units of its model M1 camera is .
To maximize its profits, how many cameras should Cannon produce each month?
__________ cameras
Question
A stone is thrown straight up from the roof of an 90-ft building. The height (in feet) of the stone at any time 
(in seconds), measured from the ground, is given by 
.
What is the maximum height the stone reaches?
__________ ft
(in seconds), measured from the ground, is given by .
What is the maximum height the stone reaches?
__________ ft
Question
A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $20,000, and the variable cost for producing 
pagers/week is 
dollars. The company realizes a revenue of 
dollars from the sale of 
pagers/week.
Find the level of production that will yield a maximum profit for the manufacturer.
pagers/week is dollars. The company realizes a revenue of dollars from the sale of pagers/week.Find the level of production that will yield a maximum profit for the manufacturer.
Question
The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is 
To maximize its profits, how many cameras should Cannon produce each month?
A) 2,250 cameras
B) 2,350 cameras
C) 2,300 cameras
D) 2,275 cameras
To maximize its profits, how many cameras should Cannon produce each month?
A) 2,250 cameras
B) 2,350 cameras
C) 2,300 cameras
D) 2,275 cameras
Question
Suppose the total cost function for manufacturing a certain product is 
dollars, where 
represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.
A) 74 units
B) 72 units
C) 80 units
D) 70 units
dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer. A) 74 units
B) 72 units
C) 80 units
D) 70 units
Question
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price/compact disc. The equation 
, where 
denotes the unit price in dollars and 
is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging
copies of this classical recording is given by 
.
To maximize its profits, how many copies should Phonola produce each month?
, where denotes the unit price in dollars and is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging
copies of this classical recording is given by .
To maximize its profits, how many copies should Phonola produce each month?
Question
The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation 
, where 
is measured in dollars and 
is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold?
A)
B)
C)
D)
E)
, where is measured in dollars and is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold?
A)
B)
C)
D)
E)
Question
Use the information summarized in the table to select the graph of
Domain: 
Intercept: x-intercept: 01 Asymptotes: x-axis and y-axis Intervals where f is ↑ and ↓: ↑ on 
↓ on 
Relative extrems: Rel. max. at 
Concavity: Downward on 
; upward 
Point of inflection: 
A) 
B) 
C) 
Domain: Intercept: x-intercept: 01 Asymptotes: x-axis and y-axis Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrems: Rel. max. at Concavity: Downward on ; upward Point of inflection: A)
B)
C)
Question
Find the horizontal and vertical asymptotes of the graph of the function. 
A) Vertical asymptote:
; Horizontal asymptote: 
B) Vertical asymptote:
; Horizontal asymptote: 
C) Vertical asymptote:
; Horizontal asymptote: 
D) Vertical asymptote:
; Horizontal asymptote: 
A) Vertical asymptote:
; Horizontal asymptote: B) Vertical asymptote:
; Horizontal asymptote: C) Vertical asymptote:
; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Question
Find the horizontal and vertical asymptotes of the graph of the function. 
A) Vertical asymptote:
; Horizontal asymptote: 
B) Vertical asymptotes:
and 
; Horizontal asymptote: 
C) Vertical asymptotes:
and 
; Horizontal asymptote: 
D) Vertical asymptote:
; Horizontal asymptote: 
A) Vertical asymptote:
; Horizontal asymptote: B) Vertical asymptotes:
and ; Horizontal asymptote: C) Vertical asymptotes:
and ; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Question
Find the horizontal and vertical asymptotes of the graph. 
A) Horizontal asymptote:
; vertical asymptote 
B) Vertical asymptote:
C) Horizontal asymptote:
D) Horizontal asymptotes:
and 
A) Horizontal asymptote:
; vertical asymptote B) Vertical asymptote:
C) Horizontal asymptote:
D) Horizontal asymptotes:
and Question
Use the information summarized in the table to select the graph of
Domain: 
Intercept: y-intercept: 03 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on 
↓ on 
Relative extrema: Rel. min. at 
; rel. ma. at 
Concavity: Downward on 
; upward on 
Point of inflection: 
A) 
B) 
C) 
Domain: Intercept: y-intercept: 03 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at ; rel. ma. at Concavity: Downward on ; upward on Point of inflection: A)
B)
C)
Question
Select the graph of the function using the curve-sketching guide. 
A) 
B) 
C) 
D) 
A)
B)
C)
D)
Question
Find the horizontal and vertical asymptotes of the graph. 
A) Horizontal asymptotes:
and 
B) Horizontal asymptote:
C) Vertical asymptote:
D) Horizontal asymptote:
; Vertical asymptote: 
A) Horizontal asymptotes:
and B) Horizontal asymptote:
C) Vertical asymptote:
D) Horizontal asymptote:
; Vertical asymptote: Question
Find the horizontal and vertical asymptotes of the graph of the function. 
A) Vertical asymptote:
; Horizontal asymptote: 
B) Vertical asymptote:
; Horizontal asymptote: 
C) Vertical asymptote:
; Horizontal asymptote: 
D) Vertical asymptote:
; Horizontal asymptote: 
A) Vertical asymptote:
; Horizontal asymptote: B) Vertical asymptote:
; Horizontal asymptote: C) Vertical asymptote:
; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Question
Using the curve-sketching guide, select the graph of the function. 
A) 
B) 
C) 
A)
B)
C)
Question
Using the curve-sketching guide, select the graph of the function. 
A) 
B) 
C) 
A)
B)
C)
Question
Find the horizontal and vertical asymptotes of the graph. 
A) Horizontal asymptote:
; Vertical asymptote: 
B) Vertical asymptotes:
and 
C) Horizontal asymptotes:
and 
; Vertical asymptote: 
D) Horizontal asymptotes:
and 
A) Horizontal asymptote:
; Vertical asymptote: B) Vertical asymptotes:
and C) Horizontal asymptotes:
and ; Vertical asymptote: D) Horizontal asymptotes:
and Question
Select the graph of the function using the curve-sketching guide. 
A) 
B) 
C) 
D) 
A)
B)
C)
D)
Question
Using the curve-sketching guide, select the graph of the function. 
A) 
B) 
C) 
A)
B)
C)
Question
One of the functions below is the derivative function of the other. Identify each of them. 
A) Functions are independent of each other
B) g is the derivative function of the function f
C) f is the derivative function of the function g
A) Functions are independent of each other
B) g is the derivative function of the function f
C) f is the derivative function of the function g
Question
Find the horizontal and vertical asymptotes of the graph. 
A) Horizontal asymptote is
, vertical asymptote is 
B) Horizontal asymptote is
, vertical asymptote is 
C) Horizontal asymptote is
, vertical asymptote is 
D) Horizontal asymptote is
, vertical asymptote is 
E) Horizontal asymptote is
, vertical asymptote is 
A) Horizontal asymptote is
, vertical asymptote is B) Horizontal asymptote is
, vertical asymptote is C) Horizontal asymptote is
, vertical asymptote is D) Horizontal asymptote is
, vertical asymptote is E) Horizontal asymptote is
, vertical asymptote is Question
Find the horizontal and vertical asymptotes of the graph of the function. 
A) Vertical asymptote:
; Horizontal asymptote: 
and 
B) Vertical asymptotes:
and 
; Horizontal asymptote: 
C) Vertical asymptote:
; Horizontal asymptote: 
D) Vertical asymptote:
; Horizontal asymptote: 
A) Vertical asymptote:
; Horizontal asymptote: and B) Vertical asymptotes:
and ; Horizontal asymptote: C) Vertical asymptote:
; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Question
Find the horizontal and vertical asymptotes of the graph of the function. 
A) Horizontal asymptote is
, vertical asymptotes are 
and 
B) Horizontal asymptotes are
and 
, vertical asymptote is 
C) Horizontal asymptote is
, vertical asymptotes are 
and 
D) Horizontal asymptote is
, vertical asymptotes are 
and 
E) Horizontal asymptote is
, vertical asymptotes are 
and 
A) Horizontal asymptote is
, vertical asymptotes are and B) Horizontal asymptotes are
and , vertical asymptote is C) Horizontal asymptote is
, vertical asymptotes are and D) Horizontal asymptote is
, vertical asymptotes are and E) Horizontal asymptote is
, vertical asymptotes are and Question
Find the horizontal and vertical asymptotes of the graph of the function. 
A) Vertical asymptotes:
, 
and 
B) Vertical asymptotes:
and 
; Horizontal asymptotes: 
and 
C) Vertical asymptote:
; Horizontal asymptotes: 
D) Vertical asymptote:
A) Vertical asymptotes:
, and B) Vertical asymptotes:
and ; Horizontal asymptotes: and C) Vertical asymptote:
; Horizontal asymptotes: D) Vertical asymptote:
Question
Use the information summarized in the table to select the graph of
Domain: 
Intercepts: x-intercepts: 0, 4 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on 
↓ on 
Relative extrema: Rel. min. at 
Concavity: Upward on 
Point of inflection: 
A) 
B) 
C) 
Domain: Intercepts: x-intercepts: 0, 4 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at Concavity: Upward on Point of inflection: A)
B)
C)
Question
Find the horizontal and vertical asymptotes of the graph. 
A) Horizontal asymptotes:
and 
B) Vertical asymptotes:
and 
; Horizontal asymptote: 
C) Horizontal asymptotes:
and 
; Vertical asymptote: 
D) Vertical asymptotes:
and 
; Horizontal asymptote: 
A) Horizontal asymptotes:
and B) Vertical asymptotes:
and ; Horizontal asymptote: C) Horizontal asymptotes:
and ; Vertical asymptote: D) Vertical asymptotes:
and ; Horizontal asymptote: 
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Deck 4: Applications of the Derivative
1
In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island. A cable is to be laid connecting the relay station with the experimental station.
If the cost of running the cable on land is $2.00/running foot and the cost of running the cable under water is $5.20/running foot, locate the point P that will result in a minimum cost (solve for x).
A)
B)
C)
D)
E)
If the cost of running the cable on land is $2.00/running foot and the cost of running the cable under water is $5.20/running foot, locate the point P that will result in a minimum cost (solve for x).
A)
B)
C)
D)
E)
2
In the diagram, S represents the position of a power relay station located on a straight coast, and E shows the location of a marine biology experimental station on an island. A cable is to be laid connecting the relay station with the experimental station.
If the cost of running the cable on land is $2.40/running foot and the cost of running the cable under water is $3.00/running foot, locate the point P that will result in a minimum cost (solve for x).
x = __________ ft
If the cost of running the cable on land is $2.40/running foot and the cost of running the cable under water is $3.00/running foot, locate the point P that will result in a minimum cost (solve for x).
x = __________ ft
4,000
3
The management of the UNICO department store has decided to enclose an 400ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing material.
If the pine board fencing costs $8/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.
A)
B)
C)
D)
If the pine board fencing costs $8/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.
A)
B)
C)
D)
4
For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of 26 in.3 and is constructed using the least amount of metal.
A)
B)
C)
D)
A)
B)
C)
D)
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5
An apple orchard has an average yield of 36 bushels of apples/tree if tree density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. How many trees should be planted in order to maximize the yield?
__________ trees
__________ trees
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6
The demand for motorcycle tires imported by Dixie Import-Export is 20,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $200, and the cost of storing each tire for a year is $2.
Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.)
A) 2,000
B) 500
C) 1,000
D) 2,500
Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.)
A) 2,000
B) 500
C) 1,000
D) 2,500
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7
A Norman window has the shape of a rectangle surmounted by a semicircle (see the accompanying figure). If a Norman window is to have a perimeter of 25 ft, what should its dimensions be in order to allow the maximum amount of light through the window?
A)
B)
C)
D)
A)
B)
C)
D)
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8
The demand for motorcycle tires imported by Dixie Import-Export is 60,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $600, and the cost of storing each tire for a year is $2.
Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.)
__________ tires
Determine how many tires should be in each shipment if the ordering and storage costs are to be minimized. (Assume that each shipment arrives just as the previous one has been sold.)
__________ tires
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9
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 8 in. long and 3 in. wide, find the dimensions of the box that will yield the maximum volume.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
The figure depicts a racetrack with ends that are semicircular in shape. The length of the track is .
Find r and lso that the area enclosed by the rectangular region of the racetrack is as large as possible.
A)
B)
C)
D)
. Find r and lso that the area enclosed by the rectangular region of the racetrack is as large as possible.
A)
B)
C)
D)
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11
An apple orchard has an average yield of 30 bushels of apples/tree if tree density is 25 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels. How many trees should be planted in order to maximize the yield?
A) 22
B) 20
C) 23
D) 21
A) 22
B) 20
C) 23
D) 21
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12
If an open box has a square base and a volume of 500 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.
A)
B)
C)
D)
A)
B)
C)
D)
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13
The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $390/person/day if exactly 20 people sign up for the cruise. However,if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $3 for each additional passenger.
Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht. What is the maximum revenue? What would be the fare/passenger in this case?
A) 75; $16,875; $225
B) 80; $16,875; $215
C) 75; $17,375; $225
D) 80; $17,375; $215
Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht. What is the maximum revenue? What would be the fare/passenger in this case?
A) 75; $16,875; $225
B) 80; $16,875; $215
C) 75; $17,375; $225
D) 80; $17,375; $215
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14
What are the dimensions of a closed rectangular box that has a square cross section, a capacity of 127 in.3 and is constructed using the least amount of material?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?
A)
B)
C)
D)
A)
B)
C)
D)
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16
A rectangular box is to have a square base and a volume of 4 ft.3. If the material for the base costs 20 cent/square foot, the material for the sides costs 30 cent/square foot, and the material for the top costs 10 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost.
A)
B)
C)
D)
A)
B)
C)
D)
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17
A truck gets 600/x mpg when driven at a constant speed of x mph (between 40 and 80 mph). If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 40 and 80 mph is it most economical to drive?
A) 60 mph
B) 80 mph
C) 75 mph
D) 40 mph
E) 45 mph
A) 60 mph
B) 80 mph
C) 75 mph
D) 40 mph
E) 45 mph
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18
A truck gets 400/x mpg when driven at a constant speed of x mph (between 40 and 70 mph). If the price of fuel is $1/gallon and the driver is paid $6/hour, at what speed between 40 and 70 mph is it most economical to drive? Round your answer to the nearest whole number.
__________ mph
__________ mph
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19
A book designer has decided that the pages of a book should have 1 in.margins at the top and bottom and in.margins on the sides. She further stipulated that each page should have an area of 27 in.2 (see the figure).
Determine the page dimensions that will result in the maximum printed area on the page, where .
A)
B)
C)
D)
in.margins on the sides. She further stipulated that each page should have an area of 27 in.2 (see the figure). Determine the page dimensions that will result in the maximum printed area on the page, where
.
A)
B)
C)
D)
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20
Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $4/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0004 for each additional bottle sold.
Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case?
A) The maximum profit is $30,000.00, the price/bottle is $3.70/bottle
B) The maximum profit is $40,000.00, the price/bottle is $4.00/bottle
C) The maximum profit is $35,000.00, the price/bottle is $3.90/bottle
D) The maximum profit is $25,000.00, the price/bottle is $3.60/bottle
E) The maximum profit is $20,000.00,the price/bottle is $4.00/bottle
Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case?
A) The maximum profit is $30,000.00, the price/bottle is $3.70/bottle
B) The maximum profit is $40,000.00, the price/bottle is $4.00/bottle
C) The maximum profit is $35,000.00, the price/bottle is $3.90/bottle
D) The maximum profit is $25,000.00, the price/bottle is $3.60/bottle
E) The maximum profit is $20,000.00,the price/bottle is $4.00/bottle
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21
A rectangular box is to have a square base and a volume of 24 ft.3. If the material for the base costs 20 cent/square foot, the material for the sides costs 10 cent/square foot, and the material for the top costs 40 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost.
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22
Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb. The estimated demand for the cookies is 1,000,000 1-lb containers. The setup cost for each production run is $250, and the manufacturing cost is $.20 for each container of cookies. The cost of storing each container of cookies over the year is $.80.
Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost?
Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost?
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23
If an open box has a square base and a volume of 864 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.
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24
Find the absolute maximum value and the absolute minimum value, if any, of the function. on
A) Absolute maximum value: ; absolute minimum value:
B) Absolute maximum value: ; absolute minimum value:
C) Absolute maximum value: ; absolute minimum value:
D) Absolute maximum value: ; absolute minimum value:
E) Absolute maximum value: ; absolute minimum value:
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) Absolute maximum value:
; absolute minimum value: E) Absolute maximum value:
; absolute minimum value: Unlock Deck
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25
The owner of the Rancho Los Feliz has 3,200 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river.
If fencing is not required along the river, what are the dimensions of the largest area that he can enclose?
What is this area?
If fencing is not required along the river, what are the dimensions of the largest area that he can enclose?
What is this area?
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k this deck
26
Find the absolute maximum value and the absolute minimum value, if any, of the given function.
A) Absolute maximum value: ; absolute minimum value: none
B) Absolute maximum value: none; absolute minimum value: 0
C) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
A) Absolute maximum value:
; absolute minimum value: noneB) Absolute maximum value: none; absolute minimum value: 0
C) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
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27
Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 90 in.
Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.
Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.
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28
Find the absolute maximum value and the absolute minimum value, if any, of the given function. on
A) Absolute maximum value: ; absolute minimum value:
B) Absolute maximum value: ; absolute minimum value:
C) Absolute maximum value: ; absolute minimum value:
D) No absolute extrema
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) No absolute extrema
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29
Find the absolute maximum value and the absolute minimum value, if any, of the given function. on
A) Absolute maximum value: 2; absolute minimum value:
B) Absolute maximum value: 3; absolute minimum value:
C) Absolute maximum value: 3; absolute minimum value:
D) No absolute extrema
on A) Absolute maximum value: 2; absolute minimum value:
B) Absolute maximum value: 3; absolute minimum value:
C) Absolute maximum value: 3; absolute minimum value:
D) No absolute extrema
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30
Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle. However, the profit from each bottle beyond 10,000 drops by $0.0002 for each additional bottle sold. Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? Round the answer to two decimal places.
The maximum profit is $__________
What would be the price/bottle in this case? Round the answer to the nearest cent.
$__________/bottle
The maximum profit is $__________
What would be the price/bottle in this case? Round the answer to the nearest cent.
$__________/bottle
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31
Find the absolute maximum value and the absolute minimum value, if any, of the function. on
A) Absolute maximum value: 0; absolute minimum value: - 48
B) Absolute maximum value: 9; absolute minimum value: - 48
C) Absolute maximum value: 5; absolute minimum value: - 4
D) Absolute maximum value: 4; absolute minimum value: - 5
E) Absolute maximum value: 9; absolute minimum value: 0
on A) Absolute maximum value: 0; absolute minimum value: - 48
B) Absolute maximum value: 9; absolute minimum value: - 48
C) Absolute maximum value: 5; absolute minimum value: - 4
D) Absolute maximum value: 4; absolute minimum value: - 5
E) Absolute maximum value: 9; absolute minimum value: 0
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32
You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist.
F defined on
A) Absolute maximum value: 0.3; absolute minimum value: -6
B) Absolute maximum value: 0.3; absolute minimum value: -2
C) Absolute maximum value: -2; absolute minimum value: -6
D) Absolute maximum value: 0.3; absolute minimum value: 0
F defined on
A) Absolute maximum value: 0.3; absolute minimum value: -6
B) Absolute maximum value: 0.3; absolute minimum value: -2
C) Absolute maximum value: -2; absolute minimum value: -6
D) Absolute maximum value: 0.3; absolute minimum value: 0
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33
Find the absolute maximum value and the absolute minimum value, if any, of the given function.
A) Absolute maximum value: 4; absolute minimum value: none
B) Absolute maximum value: 2; absolute minimum value: - 2
C) Absolute maximum value: 2; absolute minimum value: none
D) No absolute extrema
A) Absolute maximum value: 4; absolute minimum value: none
B) Absolute maximum value: 2; absolute minimum value: - 2
C) Absolute maximum value: 2; absolute minimum value: none
D) No absolute extrema
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34
Find the absolute maximum value and the absolute minimum value, if any, of the given function. on
A) Absolute maximum value: 75; absolute minimum value: - 134
B) Absolute maximum value: 26; absolute minimum value: - 134
C) Absolute maximum value: 26; absolute minimum value: - 6
D) Absolute maximum value: 75; absolute minimum value: - 6
E) No absolute extrema
on A) Absolute maximum value: 75; absolute minimum value: - 134
B) Absolute maximum value: 26; absolute minimum value: - 134
C) Absolute maximum value: 26; absolute minimum value: - 6
D) Absolute maximum value: 75; absolute minimum value: - 6
E) No absolute extrema
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35
A book designer has decided that the pages of a book should have 1 in. margins at the top and bottom and in. margins on the sides. She further stipulated that each page should have an area of 72 in.2 (see the figure).
Determine the page dimensions that will result in the maximum printed area on the page, where .
in. margins on the sides. She further stipulated that each page should have an area of 72 in.2 (see the figure).
Determine the page dimensions that will result in the maximum printed area on the page, where
.
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36
What are the dimensions of a closed rectangular box that has a square cross section, a capacity of 127 in.3 and is constructed using the least amount of material? Round the answer to two decimal places.
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37
Find the absolute maximum value and the absolute minimum value, if any, of the given function. on
A) Absolute maximum value: none; absolute minimum value: 0
B) Absolute maximum value: 0; absolute minimum value: -8
C) Absolute maximum value: 8; absolute minimum value: 0
D) No absolute extrema
on A) Absolute maximum value: none; absolute minimum value: 0
B) Absolute maximum value: 0; absolute minimum value: -8
C) Absolute maximum value: 8; absolute minimum value: 0
D) No absolute extrema
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38
Find the absolute maximum value and the absolute minimum value, if any, of the given function.
A) Absolute maximum value: ; absolute minimum value: none
B) Absolute maximum value: ; absolute minimum value: none
C) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
A) Absolute maximum value:
; absolute minimum value: noneB) Absolute maximum value:
; absolute minimum value: noneC) Absolute maximum value: none; absolute minimum value:
D) No absolute extrema
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39
You are given the graph of some function f defined on the indicated interval. Find the absolute maximum and the absolute minimum of f, if they exist. f defined on
A) Absolute maximum value: 13.0; absolute minimum value: 6.7
B) Absolute maximum value: none; absolute minimum value: none
C) Absolute maximum value: none; absolute minimum value: 6.7
D) Absolute maximum value: 13.0; absolute minimum value: none
f defined on A) Absolute maximum value: 13.0; absolute minimum value: 6.7
B) Absolute maximum value: none; absolute minimum value: none
C) Absolute maximum value: none; absolute minimum value: 6.7
D) Absolute maximum value: 13.0; absolute minimum value: none
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40
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 4 in. long and 4 in. wide, find the dimensions of the box that will yield the maximum volume.
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41
A manufacturer of tennis rackets finds that the total cost (in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation . If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
A) 5,000 rackets/day
B) 4,000 rackets/day
C) 7,000 rackets/day
D) 6,000 rackets/day
(in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation . If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
A) 5,000 rackets/day
B) 4,000 rackets/day
C) 7,000 rackets/day
D) 6,000 rackets/day
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42
Suppose the quantity demanded per week of a certain dress is related to the unit price by the demand equation , where is in dollars and is the number of dresses made.
To maximize the revenue, how many dresses should be made and sold each week?
by the demand equation , where is in dollars and is the number of dresses made.To maximize the revenue, how many dresses should be made and sold each week?
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43
The number of major crimes committed in the city between 1997 and 2004 is approximated by the function where denotes the number of crimes committed in year ( corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens with the help of the local police organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.
When was the growth in the crime rate maximal?
A) 2001
B) 2003
C) 2000
D) 2002
E) 1999
where denotes the number of crimes committed in year ( corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens with the help of the local police organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.When was the growth in the crime rate maximal?
A) 2001
B) 2003
C) 2000
D) 2002
E) 1999
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44
Find the absolute maximum value and the absolute minimum value, if any, of the given function. on
A) Absolute maximum value: ; absolute minimum value:
B) Absolute maximum value: ; absolute minimum value:
C) Absolute maximum value: ; absolute minimum value:
D) No absolute extrema
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) No absolute extrema
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45
The average speed of a vehicle on a stretch of a route between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function
, where is measured in miles per hour and is measured in hours, with corresponding to 6 A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
time = __________ A.M.
average speed = __________ mph
, where is measured in miles per hour and is measured in hours, with corresponding to 6 A.M.At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
time = __________ A.M.
average speed = __________ mph
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46
The average speed of a vehicle on a stretch of a route between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function , where is measured in miles per hour and is measured in hours, with corresponding to 6 A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
A) time = 7 A.M. ; average speed = 50 mph
B) time = 7 A.M. ; average speed = 30 mph
C) time = 7 A.M. ; average speed = 45 mph
D) time = 7 A.M. ; average speed = 40 mph
, where is measured in miles per hour and is measured in hours, with corresponding to 6 A.M.
At what time of the morning commute is the traffic moving at the slowest rate? What is the average speed of a vehicle at that time?
A) time = 7 A.M. ; average speed = 50 mph
B) time = 7 A.M. ; average speed = 30 mph
C) time = 7 A.M. ; average speed = 45 mph
D) time = 7 A.M. ; average speed = 40 mph
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47
A stone is thrown straight up from the roof of a 90-ft building. The height (in feet) of the stone at any time t (in seconds), measured from the ground, is given by
What is the maximum height the stone reaches?
A) 115 ft
B) 126 ft
C) 108 ft
D) 112 ft
What is the maximum height the stone reaches?
A) 115 ft
B) 126 ft
C) 108 ft
D) 112 ft
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48
If is defined on a closed interval , then has an absolute maximum value.
is defined on a closed interval , then has an absolute maximum value. Unlock Deck
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49
A manufacturer of tennis rackets finds that the total cost (in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation .
If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
__________ rackets/day
(in dollars) of manufacturing rackets/day is given by . Each racket can be sold at a price of dollars, where is related to by the demand equation .
If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.
__________ rackets/day
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50
The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where is measured in dollars and is measured in units of a thousand.
To yield a maximum revenue, how many watches must be sold?
__________
, where is measured in dollars and is measured in units of a thousand.To yield a maximum revenue, how many watches must be sold?
__________ Unlock Deck
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51
Find the absolute maximum value and the absolute minimum value, if any, of the given function. on
A) Absolute maximum value: ; absolute minimum value:
B) Absolute maximum value: ; absolute minimum value:
C) Absolute maximum value: ; absolute minimum value:
D) No absolute extrema
on A) Absolute maximum value:
; absolute minimum value: B) Absolute maximum value:
; absolute minimum value: C) Absolute maximum value:
; absolute minimum value: D) No absolute extrema
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52
Suppose the total cost function for manufacturing a certain product is dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.
__________ units
dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.__________ units
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53
The number of major crimes committed in the city of Bronxville between 1997 and 2004 is approximated by the function
where denotes the number of crimes committed in year ( corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens of Bronxville, with the help of the local police, organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.
Show that the growth in the crime rate was maximal in 2002, giving credence to the claim that the Neighborhood Crime Watch program was working.
where denotes the number of crimes committed in year ( corresponds to 1997). Enraged by the dramatic increase in the crime rate, the citizens of Bronxville, with the help of the local police, organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace.Show that the growth in the crime rate was maximal in 2002, giving credence to the claim that the Neighborhood Crime Watch program was working.
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54
The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling units of its model M1 camera is .
To maximize its profits, how many cameras should Cannon produce each month?
__________ cameras
units of its model M1 camera is .
To maximize its profits, how many cameras should Cannon produce each month?
__________ cameras
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55
A stone is thrown straight up from the roof of an 90-ft building. The height (in feet) of the stone at any time (in seconds), measured from the ground, is given by .
What is the maximum height the stone reaches?
__________ ft
(in seconds), measured from the ground, is given by .
What is the maximum height the stone reaches?
__________ ft
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56
A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $20,000, and the variable cost for producing pagers/week is dollars. The company realizes a revenue of dollars from the sale of pagers/week.
Find the level of production that will yield a maximum profit for the manufacturer.
pagers/week is dollars. The company realizes a revenue of dollars from the sale of pagers/week.Find the level of production that will yield a maximum profit for the manufacturer.
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57
The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is
To maximize its profits, how many cameras should Cannon produce each month?
A) 2,250 cameras
B) 2,350 cameras
C) 2,300 cameras
D) 2,275 cameras
To maximize its profits, how many cameras should Cannon produce each month?
A) 2,250 cameras
B) 2,350 cameras
C) 2,300 cameras
D) 2,275 cameras
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58
Suppose the total cost function for manufacturing a certain product is dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.
A) 74 units
B) 72 units
C) 80 units
D) 70 units
dollars, where represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer. A) 74 units
B) 72 units
C) 80 units
D) 70 units
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59
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price/compact disc. The equation , where denotes the unit price in dollars and is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging copies of this classical recording is given by .
To maximize its profits, how many copies should Phonola produce each month?
, where denotes the unit price in dollars and is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging
copies of this classical recording is given by .
To maximize its profits, how many copies should Phonola produce each month?
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60
The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where is measured in dollars and is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold?
A)
B)
C)
D)
E)
, where is measured in dollars and is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold?
A)
B)
C)
D)
E)
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61
Use the information summarized in the table to select the graph of
Domain: Intercept: x-intercept: 01 Asymptotes: x-axis and y-axis Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrems: Rel. max. at Concavity: Downward on ; upward Point of inflection:
A)
B)
C)
Domain: Intercept: x-intercept: 01 Asymptotes: x-axis and y-axis Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrems: Rel. max. at Concavity: Downward on ; upward Point of inflection: A)
B)
C)
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62
Find the horizontal and vertical asymptotes of the graph of the function.
A) Vertical asymptote: ; Horizontal asymptote:
B) Vertical asymptote: ; Horizontal asymptote:
C) Vertical asymptote: ; Horizontal asymptote:
D) Vertical asymptote: ; Horizontal asymptote:
A) Vertical asymptote:
; Horizontal asymptote: B) Vertical asymptote:
; Horizontal asymptote: C) Vertical asymptote:
; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Unlock Deck
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63
Find the horizontal and vertical asymptotes of the graph of the function.
A) Vertical asymptote: ; Horizontal asymptote:
B) Vertical asymptotes: and ; Horizontal asymptote:
C) Vertical asymptotes: and ; Horizontal asymptote:
D) Vertical asymptote: ; Horizontal asymptote:
A) Vertical asymptote:
; Horizontal asymptote: B) Vertical asymptotes:
and ; Horizontal asymptote: C) Vertical asymptotes:
and ; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Unlock Deck
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64
Find the horizontal and vertical asymptotes of the graph.
A) Horizontal asymptote: ; vertical asymptote
B) Vertical asymptote:
C) Horizontal asymptote:
D) Horizontal asymptotes: and
A) Horizontal asymptote:
; vertical asymptote B) Vertical asymptote:
C) Horizontal asymptote:
D) Horizontal asymptotes:
and Unlock Deck
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65
Use the information summarized in the table to select the graph of
Domain: Intercept: y-intercept: 03 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at ; rel. ma. at Concavity: Downward on ; upward on Point of inflection:
A)
B)
C)
Domain: Intercept: y-intercept: 03 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at ; rel. ma. at Concavity: Downward on ; upward on Point of inflection: A)
B)
C)
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66
Select the graph of the function using the curve-sketching guide.
A)
B)
C)
D)
A)
B)
C)
D)
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67
Find the horizontal and vertical asymptotes of the graph.
A) Horizontal asymptotes: and
B) Horizontal asymptote:
C) Vertical asymptote:
D) Horizontal asymptote: ; Vertical asymptote:
A) Horizontal asymptotes:
and B) Horizontal asymptote:
C) Vertical asymptote:
D) Horizontal asymptote:
; Vertical asymptote: Unlock Deck
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68
Find the horizontal and vertical asymptotes of the graph of the function.
A) Vertical asymptote: ; Horizontal asymptote:
B) Vertical asymptote: ; Horizontal asymptote:
C) Vertical asymptote: ; Horizontal asymptote:
D) Vertical asymptote: ; Horizontal asymptote:
A) Vertical asymptote:
; Horizontal asymptote: B) Vertical asymptote:
; Horizontal asymptote: C) Vertical asymptote:
; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Unlock Deck
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69
Using the curve-sketching guide, select the graph of the function.
A)
B)
C)
A)
B)
C)
Unlock Deck
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70
Using the curve-sketching guide, select the graph of the function.
A)
B)
C)
A)
B)
C)
Unlock Deck
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71
Find the horizontal and vertical asymptotes of the graph.
A) Horizontal asymptote: ; Vertical asymptote:
B) Vertical asymptotes: and
C) Horizontal asymptotes: and ; Vertical asymptote:
D) Horizontal asymptotes: and
A) Horizontal asymptote:
; Vertical asymptote: B) Vertical asymptotes:
and C) Horizontal asymptotes:
and ; Vertical asymptote: D) Horizontal asymptotes:
and Unlock Deck
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72
Select the graph of the function using the curve-sketching guide.
A)
B)
C)
D)
A)
B)
C)
D)
Unlock Deck
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Unlock Deck
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73
Using the curve-sketching guide, select the graph of the function.
A)
B)
C)
A)
B)
C)
Unlock Deck
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74
One of the functions below is the derivative function of the other. Identify each of them.
A) Functions are independent of each other
B) g is the derivative function of the function f
C) f is the derivative function of the function g
A) Functions are independent of each other
B) g is the derivative function of the function f
C) f is the derivative function of the function g
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75
Find the horizontal and vertical asymptotes of the graph.
A) Horizontal asymptote is , vertical asymptote is
B) Horizontal asymptote is , vertical asymptote is
C) Horizontal asymptote is , vertical asymptote is
D) Horizontal asymptote is , vertical asymptote is
E) Horizontal asymptote is , vertical asymptote is
A) Horizontal asymptote is
, vertical asymptote is B) Horizontal asymptote is
, vertical asymptote is C) Horizontal asymptote is
, vertical asymptote is D) Horizontal asymptote is
, vertical asymptote is E) Horizontal asymptote is
, vertical asymptote is Unlock Deck
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76
Find the horizontal and vertical asymptotes of the graph of the function.
A) Vertical asymptote: ; Horizontal asymptote: and
B) Vertical asymptotes: and ; Horizontal asymptote:
C) Vertical asymptote: ; Horizontal asymptote:
D) Vertical asymptote: ; Horizontal asymptote:
A) Vertical asymptote:
; Horizontal asymptote: and B) Vertical asymptotes:
and ; Horizontal asymptote: C) Vertical asymptote:
; Horizontal asymptote: D) Vertical asymptote:
; Horizontal asymptote: Unlock Deck
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77
Find the horizontal and vertical asymptotes of the graph of the function.
A) Horizontal asymptote is , vertical asymptotes are and
B) Horizontal asymptotes are and , vertical asymptote is
C) Horizontal asymptote is , vertical asymptotes are and
D) Horizontal asymptote is , vertical asymptotes are and
E) Horizontal asymptote is , vertical asymptotes are and
A) Horizontal asymptote is
, vertical asymptotes are and B) Horizontal asymptotes are
and , vertical asymptote is C) Horizontal asymptote is
, vertical asymptotes are and D) Horizontal asymptote is
, vertical asymptotes are and E) Horizontal asymptote is
, vertical asymptotes are and Unlock Deck
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78
Find the horizontal and vertical asymptotes of the graph of the function.
A) Vertical asymptotes: , and
B) Vertical asymptotes: and ; Horizontal asymptotes: and
C) Vertical asymptote: ; Horizontal asymptotes:
D) Vertical asymptote:
A) Vertical asymptotes:
, and B) Vertical asymptotes:
and ; Horizontal asymptotes: and C) Vertical asymptote:
; Horizontal asymptotes: D) Vertical asymptote:
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79
Use the information summarized in the table to select the graph of
Domain: Intercepts: x-intercepts: 0, 4 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at Concavity: Upward on Point of inflection:
A)
B)
C)
Domain: Intercepts: x-intercepts: 0, 4 Asymptotes: None Intervals where f is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at Concavity: Upward on Point of inflection: A)
B)
C)
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80
Find the horizontal and vertical asymptotes of the graph.
A) Horizontal asymptotes: and
B) Vertical asymptotes: and ; Horizontal asymptote:
C) Horizontal asymptotes: and ; Vertical asymptote:
D) Vertical asymptotes: and ; Horizontal asymptote:
A) Horizontal asymptotes:
and B) Vertical asymptotes:
and ; Horizontal asymptote: C) Horizontal asymptotes:
and ; Vertical asymptote: D) Vertical asymptotes:
and ; Horizontal asymptote: Unlock Deck
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Unlock Deck
Unlock for access to all 152 flashcards in this deck.
