Question 1

Find the graph of the derivative of the function.

Accepted Answer

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

Question 2

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

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 3

A stone is thrown straight up from the roof of an 60-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?
__________ ft

Accepted Answer

The answer of A stone is thrown straight up from...

Question 4

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 $3.60/running foot and the cost of running the cable under water is $6.00/running foot, locate the point P that will result in a minimum cost (solve for x).   __________ ft

Accepted Answer

The answer of In the diagram, S represents the position...

Question 5

The demand for motorcycle tires imported by Dixie Import-Export is 30,000/year and may be assumed to be uniform throughout the year. The cost of ordering a shipment of tires is $300, 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

Accepted Answer

The answer of The demand for motorcycle tires imported by...

Question 6

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   and is constructed using the least amount of metal.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Accepted Answer

A)  Relative maximum:   ; Relative minimum:
  
B)  Relative maximum:   ; Relative minimum:
  
C)  Relative maximum:   ; Relative minimum:
  
D)  Relative maximum:   ; Relative minimum:
  
E)  none 
A)  Relative maximum:   ; Relative minimum:
  
B)  Relative maximum:   ; Relative minimum:
  
C)  Relative maximum:   ; Relative minimum:
  
D)  Relative maximum:   ; Relative minimum:
  
E)  none

Question 8

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Accepted Answer

A)  Relative minimum:   
B)  Relative maximum:   
C)  Relative minimum:   
D)  Relative maximum:   
E)  none 
A)  Relative minimum:   
B)  Relative maximum:   
C)  Relative minimum:   
D)  Relative maximum:   
E)  none

Question 9

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 p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price.
The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by   .
To maximize its profits, how many copies should Phonola produce each month? Hint: The revenue is   , and the profit is   .

Accepted Answer

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

Question 10

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

Accepted Answer

A)  Increasing on   
B)  Increasing on   , decreasing on
  
C)  Increasing on   , decreasing on
  
D)  Increasing on   , decreasing on
  
A)  Increasing on   
B)  Increasing on   , decreasing on
  
C)  Increasing on   , decreasing on
  
D)  Increasing on   , decreasing on

Question 11

A rectangular box is to have a square base and a volume of 4   . 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.

Accepted Answer

The answer of A rectangular box is to have a...

Question 12

The level of ozone, an invisible gas that irritates and impairs breathing, present in the atmosphere on a certain May day in the city was approximated by   , where   is measured in pollutant standard index (PSI) and   is measured in hours, with   corresponding to   a.m.
Use the second derivative test to show that the function   has a relative maximum at approximately   . Interpret your results.

Accepted Answer

The first two derivatives of @#IMG-DLM& are given

Question 13

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?

Accepted Answer

A)  10,000 cameras 
B)  10,100 cameras 
C)  10,050 cameras 
D)  10,025 cameras 
A)  10,000 cameras 
B)  10,100 cameras 
C)  10,050 cameras 
D)  10,025 cameras

Question 14

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

Accepted Answer

A)  Vertical asymptote: x = 4; Horizontal asymptote: y = -1 
B)  Vertical asymptote: x = 0; Horizontal asymptote: y = -1 
C)  Vertical asymptote: x = -1; Horizontal asymptote: y = 4 
D)  Vertical asymptote: x = -1; Horizontal asymptote: y = 0 
A)  Vertical asymptote: x = 4; Horizontal asymptote: y = -1 
B)  Vertical asymptote: x = 0; Horizontal asymptote: y = -1 
C)  Vertical asymptote: x = -1; Horizontal asymptote: y = 4 
D)  Vertical asymptote: x = -1; Horizontal asymptote: y = 0

Question 15

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none.   Relative maxima: __________
Relative minima: __________

Accepted Answer

The answer of Find the relative maxima and relative minima,...

Question 16

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If f is increasing on (a, b), then   for each x in (a, b).

Accepted Answer

A)  False. For example,  
  increasing on
  but
  
B)  True. This follows from the definition. 
C)  False. For example,  
  increasing on any
  but
  
A)  False. For example,  
  increasing on
  but
  
B)  True. This follows from the definition. 
C)  False. For example,  
  increasing on any
  but

Question 17

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Accepted Answer

A)  Relative maximum at (0, 0) 
B)  Relative minimum at (0, 0) 
C)  Relative minimum at (   , 0) 
D)  Relative maximum at (   ) 
E)  Relative minimum at (   ) 
A)  Relative maximum at (0, 0) 
B)  Relative minimum at (0, 0) 
C)  Relative minimum at (   , 0) 
D)  Relative maximum at (   ) 
E)  Relative minimum at (   )

Question 18

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.

Accepted Answer

The answer of By cutting away identical squares from each...

Question 19

One of the functions below is the derivative function of the other. Identify each of them.

Accepted Answer

g is the d

Question 20

Using the curve-sketching guide, select the graph of the function.

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Find the graph of the derivative of the function.

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

A stone is thrown straight up from the roof of an 60-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? __________ ft

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 and is constructed using the least amount of metal.

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

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?

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

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. Relative maxima: Relative minima:

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If f is increasing on (a, b), then for each x in (a, b).

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

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.

One of the functions below is the derivative function of the other. Identify each of them.

Using the curve-sketching guide, select the graph of the function.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 4: Applications of the Derivative

Find the graph of the derivative of the function.

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

A stone is thrown straight up from the roof of an 60-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? __________ ft

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 and is constructed using the least amount of metal.

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

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?

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

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. Relative maxima: __________ Relative minima: __________

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If f is increasing on (a, b), then for each x in (a, b).

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable.

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.

One of the functions below is the derivative function of the other. Identify each of them.

Using the curve-sketching guide, select the graph of the function.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Find the relative maxima and relative minima, if any, of the function. Otherwise, answer none. Relative maxima: Relative minima: