Question 1

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

Accepted Answer

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

Question 2

You are given the graph of a function f.Determine the intervals where f is concave downward.

Accepted Answer

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

Question 3

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation   , where p is measured in dollars and x is measured in units of a thousand.
To yield a maximum revenue, how many watches must be sold?   __________

Accepted Answer

10

Question 4

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 
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 5

The figure depicts a racetrack with ends that are semicircular in shape.The length of the track is   .   Find   and   so that the area enclosed by the rectangular region of the racetrack is as large as possible.

Accepted Answer

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

Question 6

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 $2.50/running foot and the cost of running the cable under water is $6.50/running foot, locate the point P that will result in a minimum cost (solve for x).

Accepted Answer

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

Question 7

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 the graph of f is concave downward on (a, b), then the graph of - f is concave upward on (a, b).

Accepted Answer

The statement is true.If the graph of f

Question 8

Find the graph of the derivative of the function.

Accepted Answer

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

Question 9

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

Accepted Answer

A) No relative minima; Relative maximum f (3) = - 5 
B) Relative maximum: f (3) = -22; Relative minimum f (0) = - 5 
C) Relative minimum: f (3) = -22; No relative maxima 
D) No relative maxima or minima 
A) No relative minima; Relative maximum f (3) = - 5 
B) Relative maximum: f (3) = -22; Relative minimum f (0) = - 5 
C) Relative minimum: f (3) = -22; No relative maxima 
D) No relative maxima or minima

Question 10

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

Accepted Answer

A) g is the derivative function of the function f 
B) f is the derivative function of the function g 
C) Functions are independent of each other 
A) g is the derivative function of the function f 
B) f is the derivative function of the function g 
C) Functions are independent of each other

Question 11

Determine where the function is concave upward.

Accepted Answer

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

Question 12

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

Accepted Answer

A) Relative maximum: f (1) = 11 
B) Relative maximum: f (0) = 5 
C) Relative minimum: f (0) = 5 
D) Relative minimum: f (1) = 11 
E) none 
A) Relative maximum: f (1) = 11 
B) Relative maximum: f (0) = 5 
C) Relative minimum: f (0) = 5 
D) Relative minimum: f (1) = 11 
E) none

Question 13

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 14

Determine where the function is concave upward.

Accepted Answer

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

Question 15

Suppose the quantity demanded per week of a certain dress is related to the unit price p by the demand equation   , where p is in dollars and x is the number of dresses made.
To maximize the revenue, how many dresses should be made and sold each week? (Hint: R(x) = px.) Round the answer to the nearest integer.
__________ dresses

Accepted Answer

The answer of Suppose the quantity demanded per week of...

Question 16

Find the inflection points, if any, of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E) none 
A)    
B)    
C)    
D)    
E) none

Question 17

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

Accepted Answer

A) Vertical asymptote: x = -2; Horizontal asymptote: y = 1 
B) Vertical asymptote: x = -2; Horizontal asymptote: y = 3 
C) Vertical asymptote: x = -2; Horizontal asymptote: y = 0 
D) Vertical asymptote: x = 3; Horizontal asymptote: y = -2 
A) Vertical asymptote: x = -2; Horizontal asymptote: y = 1 
B) Vertical asymptote: x = -2; Horizontal asymptote: y = 3 
C) Vertical asymptote: x = -2; Horizontal asymptote: y = 0 
D) Vertical asymptote: x = 3; Horizontal asymptote: y = -2

Question 18

If an open box has a square base and a volume of 864   and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

Accepted Answer

The answer of If an open box has a square...

Question 19

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

Accepted Answer

A) Absolute maximum value: 0; absolute minimum value: - 48 
B) Absolute maximum value: 5; absolute minimum value: - 4 
C) Absolute maximum value: 4; absolute minimum value: - 5 
D) Absolute maximum value: 9; absolute minimum value: - 48 
E) Absolute maximum value: 9; absolute minimum value: 0 
A) Absolute maximum value: 0; absolute minimum value: - 48 
B) Absolute maximum value: 5; absolute minimum value: - 4 
C) Absolute maximum value: 4; absolute minimum value: - 5 
D) Absolute maximum value: 9; absolute minimum value: - 48 
E) Absolute maximum value: 9; absolute minimum value: 0

Question 20

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.

Accepted Answer

A) Absolute maximum value: 6; absolute minimum value: 0 
B) Absolute maximum value: 4; absolute minimum value: - 1 
C) Absolute maximum value: 3; absolute minimum value: - 1 
D) Absolute maximum value: 6; absolute minimum value: - 1 
A) Absolute maximum value: 6; absolute minimum value: 0 
B) Absolute maximum value: 4; absolute minimum value: - 1 
C) Absolute maximum value: 3; absolute minimum value: - 1 
D) Absolute maximum value: 6; absolute minimum value: - 1

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

You are given the graph of a function f.Determine the intervals where f is concave downward.

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where p is measured in dollars and x is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? __________

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

The figure depicts a racetrack with ends that are semicircular in shape.The length of the track is . Find and so that the area enclosed by the rectangular region of the racetrack is as large as possible.

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 the graph of f is concave downward on (a, b), then the graph of - f is concave upward on (a, b).

Find the graph of the derivative of the function.

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

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

Determine where the function is concave upward.

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

Determine where the function is concave upward.

Find the inflection points, if any, of the function.

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

If an open box has a square base and a volume of 864 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

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

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.

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

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

You are given the graph of a function f.Determine the intervals where f is concave downward.

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where p is measured in dollars and x is measured in units of a thousand. To yield a maximum revenue, how many watches must be sold? __________

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

The figure depicts a racetrack with ends that are semicircular in shape.The length of the track is . Find and so that the area enclosed by the rectangular region of the racetrack is as large as possible.

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 the graph of f is concave downward on (a, b), then the graph of - f is concave upward on (a, b).

Find the graph of the derivative of the function.

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

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

Determine where the function is concave upward.

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

Determine where the function is concave upward.

Find the inflection points, if any, of the function.

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

If an open box has a square base and a volume of 864 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.

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

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.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters