Question 1

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Accepted Answer

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 2

Find the relative maxima and relative minima, if any, of the function.

Accepted Answer

A) No relative maximum; Relative minima  
B) No relative maximum or minimum 
C) Relative minimum:  ; No relative maximum 
D) Relative maximum:  ; Relative minima
 
E) Relative maximum:  ; No relative minimum

Question 3

Find the horizontal and vertical asymptotes of the graph of the function.

Accepted Answer

A) Vertical asymptotes: t = 1 and t = -1; Horizontal asymptote: y = -1 
B) Vertical asymptote: t = 2; Horizontal asymptote: y = -1 
C) Vertical asymptotes: t = 2 and t = - 2; Horizontal asymptote: y = 1 
D) Vertical asymptote: t = 4; Horizontal asymptote: y = 1

Question 4

Find the horizontal and vertical asymptotes of the graph of the function.(You need not sketch the graph.)  Horizontal asymptote(s) __________
Vertical asymptote(s) __________

Accepted Answer

The answer of Find the horizontal and vertical asymptotes of...

Question 5

Find the relative maxima and relative minima, if any, of the function.

Accepted Answer

A) Relative minimum: g(2) = 2, Relative maximum: g(0) = 6 
B) Relative maximum: g(2) = - 6, No relative minima 
C) No relative maxima, Relative minimum: g(2) = - 6 
D) No relative maxima or minima.

Question 6

An efficiency study conducted for a company showed that the number of devices assembled by the average worker t hr after starting work at 8 A.M.10 A.M.is given by
  At what time during the morning shift is the average worker performing at peak efficiency?
At __________

Accepted Answer

The answer of An efficiency study conducted for a company...

Question 7

The management of the UNICO department store has decided to enclose an 300  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 $6/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.

Accepted Answer

A)   
B)   
C)   
D)

Question 8

An apple orchard has an average yield of 48 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

Accepted Answer

The answer of An apple orchard has an average yield...

Question 9

The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $600/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 $4 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?

Accepted Answer

A) 85; $28,400; $340 
B) 90; $28,900; $350 
C) 90; $28,400; $350 
D) 85; $28,900; $340

Question 10

Use the information summarized in the table to select the graph of f.

Accepted Answer

A)   
B)   
C)

Question 11

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 102 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.What is the volume of such a package? (Hint: The length plus the girth is  (see the figure)).

Accepted Answer

A)   ,  
B)   ,  
C)   ,  
D)   ,  
E)   ,

Question 12

Find the inflection points, if any, of the function.Otherwise, answer no solution.

Accepted Answer

The answer of Find the inflection points, if any, of...

Question 13

Find the inflection points, if any, of the following function.Otherwise, answer no solution.

Accepted Answer

The answer of Find the inflection points, if any, of...

Question 14

Find the inflection points, if any, of the function.Otherwise, answer no solution.

Accepted Answer

The answer of Find the inflection points, if any, of...

Question 15

Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter.

Accepted Answer

A) Dimensions are 13 ft.by 11 ft. 
B) Dimensions are 15ft.by 14 ft. 
C) Dimensions are 12 ft.by 12 ft. 
D) Dimensions are 10 ft.by 14 ft. 
E) Dimensions are 9 ft.by 13 ft.

Question 16

A division of Chapman Corporation manufactures a pager.The weekly fixed cost for the division is $20,000, and the variable cost for producing x pagers/week is  dollars. The company realizes a revenue of  dollars from the sale of x pagers/week.
Find the level of production that will yield a maximum profit for the manufacturer.(Hint: Use the quadratic formula.)

Accepted Answer

A) 1,316 pagers/week 
B) 1,666 pagers/week 
C) 1,616 pagers/week 
D) 1,542 pagers/week

Question 17

A cylindrical container for storing radioactive waste is to be constructed from lead and have a thickness of 6 in.(see the figure).If the volume of the outside cylinder is to be  , find the radius and the height of the inside cylinder that will result in a container of maximum storage capacity.  Hint: Show that the storage capacity (inside volume) is given by

Accepted Answer

A) r =  ft.; h = 2 ft. 
B) r =  ft.; h = 3 ft. 
C) r =  ft.; h = 2 ft. 
D) r =  ft.; h = 3 ft.

Question 18

Answer true or false.
If f is defined on a closed interval  , then f has an absolute maximum value.

Accepted Answer

A) True 
 B)False

Question 19

Find the relative maxima and relative minima, if any, of the function.

Accepted Answer

A) No relative maximum; Relative minima f (0) = - 3 
B) Relative maximum: f (0) = 0; No relative minimum 
C) Relative maximum: f (3) = 0; Relative minima f (0) = - 3 
D) No relative maximum or minimum

Question 20

The total annual revenue  of the Miramar Resorts Hotel is related to the amount of money  the hotel spends on advertising its services by the function  where both  and  are measured in thousands of dollars. Use this function to:
A. Find the interval where the graph of  is concave upward and the interval where the graph of  is concave downward.
B. Find the inflection point of  .
C. Determine if it would it be more beneficial for the hotel to increase its advertising budget slightly when the budget is $90,000 or when it is $110,000.

Accepted Answer

A) concave upward on  ;
Concave downward on
 ;
Inflection point is
 ;
 
B) concave downward on  ;
Concave upward on
 ;
Inflection point is
 ;
 
C) concave upward on  ;
Concave downward on
 ;
Inflection point is
 ;
 
D) concave downward on  ;
Concave upward on
 ;
Inflection point is
 ;
 
E) concave upward on  ;
Concave downward on
 ;
Inflection point is
 ;

Exam 4: Applications of the Derivative

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Find the relative maxima and relative minima, if any, of the function.

Find the horizontal and vertical asymptotes of the graph of the function.

Find the horizontal and vertical asymptotes of the graph of the function.(You need not sketch the graph.) Horizontal asymptote(s) Vertical asymptote(s)

Find the relative maxima and relative minima, if any, of the function.

An efficiency study conducted for a company showed that the number of devices assembled by the average worker t hr after starting work at 8 A.M.10 A.M.is given by At what time during the morning shift is the average worker performing at peak efficiency? At __________

An apple orchard has an average yield of 48 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

Use the information summarized in the table to select the graph of f.

Find the inflection points, if any, of the function.Otherwise, answer no solution.

Find the inflection points, if any, of the following function.Otherwise, answer no solution.

Find the inflection points, if any, of the function.Otherwise, answer no solution.

Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter.

Answer true or false. If f is defined on a closed interval , then f has an absolute maximum value.

Find the relative maxima and relative minima, if any, of the function.

Exam 4: Applications of the Derivative

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

Find the relative maxima and relative minima, if any, of the function.

Find the horizontal and vertical asymptotes of the graph of the function.

Find the horizontal and vertical asymptotes of the graph of the function.(You need not sketch the graph.) Horizontal asymptote(s) __________ Vertical asymptote(s) __________

Find the relative maxima and relative minima, if any, of the function.

An efficiency study conducted for a company showed that the number of devices assembled by the average worker t hr after starting work at 8 A.M.10 A.M.is given by At what time during the morning shift is the average worker performing at peak efficiency? At __________

An apple orchard has an average yield of 48 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

Use the information summarized in the table to select the graph of f.

Find the inflection points, if any, of the function.Otherwise, answer no solution.

Find the inflection points, if any, of the following function.Otherwise, answer no solution.

Find the inflection points, if any, of the function.Otherwise, answer no solution.

Find the dimensions of a rectangle of area 144 sq ft that has the smallest possible perimeter.

Answer true or false. If f is defined on a closed interval , then f has an absolute maximum value.

Find the relative maxima and relative minima, if any, of the function.

Find the horizontal and vertical asymptotes of the graph of the function.(You need not sketch the graph.) Horizontal asymptote(s) Vertical asymptote(s)