Question 1

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

Accepted Answer

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

Question 2

Determine where the function is concave upward.

Accepted Answer

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

Question 3

The average cost per disc (in dollars) incurred by Herald Records in pressing x DVDs is given by the average cost function.   Find the horizontal asymptote of   and the limiting value of the average cost.

Accepted Answer

A)  Horizontal asymptote is   , the limiting value is
  
B)  Horizontal asymptote is   , the limiting value is
  
C)  Horizontal asymptote is   , the limiting value is
  
D)  Horizontal asymptote is   , the limiting value is
  
E)  Horizontal asymptote is   , the limiting value is
  
A)  Horizontal asymptote is   , the limiting value is
  
B)  Horizontal asymptote is   , the limiting value is
  
C)  Horizontal asymptote is   , the limiting value is
  
D)  Horizontal asymptote is   , the limiting value is
  
E)  Horizontal asymptote is   , the limiting value is

Question 4

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by   To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?

Accepted Answer

A)  88 units are rented and the maximum monthly profit realizable is $23,720 
B)  22 units are rented and the maximum monthly profit realizable is $47,440 
C)  88 units are rented and the maximum monthly profit realizable ix $11,860 
D)  88 units are rented and the maximum monthly profit realizable is $47,440 
E)  44 units are rented and the maximum monthly profit realizable is $47,440 
A)  88 units are rented and the maximum monthly profit realizable is $23,720 
B)  22 units are rented and the maximum monthly profit realizable is $47,440 
C)  88 units are rented and the maximum monthly profit realizable ix $11,860 
D)  88 units are rented and the maximum monthly profit realizable is $47,440 
E)  44 units are rented and the maximum monthly profit realizable is $47,440

Question 5

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 6

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

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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 10

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 11

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 12

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

Accepted Answer

A)  Absolute maximum value: none; absolute minimum value:   
B)  Absolute maximum value:   ; absolute minimum value: none 
C)  Absolute maximum value:   ; absolute minimum value: none 
D)  No absolute extrema 
A)  Absolute maximum value: none; absolute minimum value:   
B)  Absolute maximum value:   ; absolute minimum value: none 
C)  Absolute maximum value:   ; absolute minimum value: none 
D)  No absolute extrema

Question 13

Suppose the total cost function for manufacturing a certain product is   dollars, where x represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.

Accepted Answer

A)  46 units 
B)  50 units 
C)  40 units 
D)  44 units 
A)  46 units 
B)  50 units 
C)  40 units 
D)  44 units

Question 14

The height (in feet) attained by a rocket t sec into flight is given by the function   . When is the rocket rising and when is it descending?

Accepted Answer

A)  The rocket is rising on the interval (0,17) and it is descending on the interval (17, t) where t is some positive number more than 17. 
B)  The rocket is rising on the interval (0,58) and it is descending on the interval (58, t) where t is some positive number more than 58. 
C)  The rocket is rising on the interval (0,21) and it is descending on the interval (21, t) where t is some positive number more than 21. 
D)  The rocket is rising on the interval (0,45) and it is descending on the interval (45, t) where t is some positive number more than 45. 
A)  The rocket is rising on the interval (0,17) and it is descending on the interval (17, t) where t is some positive number more than 17. 
B)  The rocket is rising on the interval (0,58) and it is descending on the interval (58, t) where t is some positive number more than 58. 
C)  The rocket is rising on the interval (0,21) and it is descending on the interval (21, t) where t is some positive number more than 21. 
D)  The rocket is rising on the interval (0,45) and it is descending on the interval (45, t) where t is some positive number more than 45.

Question 15

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 16

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

Accepted Answer

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

Question 17

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 18

The graph of the function f shown in the accompanying figure gives the elevation of that part of the Boston Marathon course that includes the notorious Heartbreak Hill. Determine the intervals (stretches of the course) where the function f is increasing (the runner is laboring), where it is constant (the runner is taking a breather), and where it is decreasing (the runner is coasting).

Accepted Answer

A)  Decreasing on   , increasing on
  , and constant on
  
B)  Decreasing on   , increasing on
  , and constant on
  
C)  Decreasing on   , increasing on
  , and constant on
  
A)  Decreasing on   , increasing on
  , and constant on
  
B)  Decreasing on   , increasing on
  , and constant on
  
C)  Decreasing on   , increasing on
  , and constant on

Question 19

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 20

Find the horizontal and vertical asymptotes of the graph.

Accepted Answer

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

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

Determine where the function is concave upward.

The average cost per disc (in dollars) incurred by Herald Records in pressing x DVDs is given by the average cost function. Find the horizontal asymptote of and the limiting value of the average cost.

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?

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

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.

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

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

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

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

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

Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.

The height (in feet) attained by a rocket t sec into flight is given by the function . When is the rocket rising and when is it descending?

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

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

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

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 horizontal and vertical asymptotes of the graph.

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

Determine where the function is concave upward.

The average cost per disc (in dollars) incurred by Herald Records in pressing x DVDs is given by the average cost function. Find the horizontal asymptote of and the limiting value of the average cost.

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by To maximize the monthly rental profit, how many units should be rented out? What is the maximum monthly profit realizable?

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

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.

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

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

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

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

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

Suppose the total cost function for manufacturing a certain product is dollars, where x represents the number of units produced. Find the level of production that will minimize the average cost. Round the answer to the nearest integer.

The height (in feet) attained by a rocket t sec into flight is given by the function . When is the rocket rising and when is it descending?

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

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

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

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 horizontal and vertical asymptotes of the graph.

Preliminaries

Functions, Limits and the Derivative

Differentiation

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

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