Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) Relative minimum:   
B) Relative maximum:   
C) Relative maximum:   
D) Relative minimum:   
E) Relative minimum:   
A) Relative minimum:   
B) Relative maximum:   
C) Relative maximum:   
D) Relative minimum:   
E) Relative minimum:

Question 3

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 4

A wooden beam has a rectangular cross section of height   in.and width   in.(see the figure).The strength   of the beam is directly proportional to its width and the square of its height. What are the dimensions of the cross section of the strongest beam that can be cut from a round log of diameter 24 in.? Hint:   , where   is a constant of proportionality.

Accepted Answer

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

Question 5

A truck gets   mpg when driven at a constant speed of x mph (between 50 and 70 mph).If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 50 and 70 mph is it most economical to drive?
__________ mph

Accepted Answer

The answer of A truck gets   mpg when...

Question 6

A city's main well was recently found to be contaminated with trichloroethylene (a cancer-causing chemical) as a result of an abandoned chemical dump leaching chemicals into the water.A proposal submitted to the city council indicated that the cost, measured in millions of dollars, of removing x% of the toxic pollutants is given by   . Find the vertical asymptote of C(x).Is it possible to remove 99% of the toxic pollutant from the water?

Accepted Answer

A) Vertical asymptote: x = 0.4 It is possible to remove 99% of the toxic pollutant from the water 
B) Vertical asymptote: x = 0.4 It is not possible to remove 99% of the toxic pollutant from the water 
C) Vertical asymptote: x = 100 It is not possible to remove 99% of the toxic pollutant from the water 
D) Vertical asymptote: x = 100 It is possible to remove 99% of the toxic pollutant from the water 
A) Vertical asymptote: x = 0.4 It is possible to remove 99% of the toxic pollutant from the water 
B) Vertical asymptote: x = 0.4 It is not possible to remove 99% of the toxic pollutant from the water 
C) Vertical asymptote: x = 100 It is not possible to remove 99% of the toxic pollutant from the water 
D) Vertical asymptote: x = 100 It is possible to remove 99% of the toxic pollutant from the water

Question 7

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

Question 8

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

Accepted Answer

A) Absolute maximum value: 2; absolute minimum value: - 2 
B) Absolute maximum value: 2; absolute minimum value: none 
C) Absolute maximum value: 4; absolute minimum value: none 
D) No absolute extrema 
A) Absolute maximum value: 2; absolute minimum value: - 2 
B) Absolute maximum value: 2; absolute minimum value: none 
C) Absolute maximum value: 4; absolute minimum value: none 
D) No absolute extrema

Question 9

The number of major crimes committed in the city between 1997 and 2004 is approximated by the function   where N(t) denotes the number of crimes committed in year t (   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.
Show that the growth in the crime rate was maximal in 2003, giving credence to the claim that the Neighborhood Crime Watch program was working.

Accepted Answer

The crime rate is @#IMG-DLM& .Derivative

Question 10

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 find the approximate value of   where the function   has a relative maximum.Round to the nearest integer.

Accepted Answer

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

Question 11

Determine the relative maxima and relative minima, if any.

Accepted Answer

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

Question 12

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 = 2 
B) Vertical asymptote: t = 3; Horizontal asymptote: y = 1 
C) Vertical asymptote: t = -1; Horizontal asymptote: y = 3 and y = 2 
D) Vertical asymptote: t = -1; Horizontal asymptote: y = 3 
A) Vertical asymptotes: t = -1 and t = 1; Horizontal asymptote: y = 2 
B) Vertical asymptote: t = 3; Horizontal asymptote: y = 1 
C) Vertical asymptote: t = -1; Horizontal asymptote: y = 3 and y = 2 
D) Vertical asymptote: t = -1; Horizontal asymptote: y = 3

Question 13

Determine where the function is concave upward and where it is concave downward.

Accepted Answer

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

Question 14

Find the inflection points of the following function.

Accepted Answer

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

Question 15

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 16

Sketch the graph of the function having the given properties.   ,   ,   ,   ,   on   ,   on   , inflection point at

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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   .
__________
What is the limiting value of the average cost?
__________

Accepted Answer

The answer of The average cost per disc (in dollars)...

Question 20

The average speed of a vehicle on a stretch of a route between 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
A.M.and 10
A.M.on a typical weekday is approximated by the function
   , where f (t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6

Accepted Answer

The answer of The average speed of a vehicle on...

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

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

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

A truck gets mpg when driven at a constant speed of x mph (between 50 and 70 mph).If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 50 and 70 mph is it most economical to drive? __________ mph

Find the horizontal and vertical asymptotes of the graph.

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

Determine the relative maxima and relative minima, if any.

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

Determine where the function is concave upward and where it is concave downward.

Find the inflection points of the following function.

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.

Sketch the graph of the function having the given properties. , , , , on , on , inflection point at

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

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

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 . What is the limiting value of the average cost?

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

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

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

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

A truck gets mpg when driven at a constant speed of x mph (between 50 and 70 mph).If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 50 and 70 mph is it most economical to drive? __________ mph

Find the horizontal and vertical asymptotes of the graph.

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

Determine the relative maxima and relative minima, if any.

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

Determine where the function is concave upward and where it is concave downward.

Find the inflection points of the following function.

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.

Sketch the graph of the function having the given properties. , , , , on , on , inflection point at

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

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

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 . __________ What is the limiting value of the average cost? __________

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 minima: Relative maxima:

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

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 . What is the limiting value of the average cost?