Question 1

Sketch a graph of a single function that has these properties.
-Find

Accepted Answer

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

Question 2

Provide an appropriate response.
-Use a graphing utility to approximate the intervals where f(x) is decreasing and intervals where f(x) is increasing for the function   Round your answer to two decimal places.

Accepted Answer

A)    decreasing on (-0.82, 0.62) 
B)    and (0.62, 2.45); increasing on (-0.82, 0.62) and (2.45, ∞) 
C)    ) and (0.62, 2.45); decreasing on (-0.82, 0.62) and (2.45, ∞) 
D)    increasing on (-0.82, 0.62) 
A)    decreasing on (-0.82, 0.62) 
B)    and (0.62, 2.45); increasing on (-0.82, 0.62) and (2.45, ∞) 
C)    ) and (0.62, 2.45); decreasing on (-0.82, 0.62) and (2.45, ∞) 
D)    increasing on (-0.82, 0.62) B

Question 3

Find the limit, if it exists.
-Find   .

Accepted Answer

A)  3 
B)  108 
C)  0 
D)  81 
A)  3 
B)  108 
C)  0 
D)  81 B

Question 4

Find the limit, if it exists.
-

Accepted Answer

A)  -6 
B)  0 
C)    
D)    
A)  -6 
B)  0 
C)    
D)

Question 5

Provide an appropriate response.
-Given   find the values of x corresponding to local maxima and local minima.

Accepted Answer

A)  local minimum at x = -4 (no local maximum) 
B)  local maximum at x = -4, local minimum at x = 4 
C)  no local maximum or minimum 
D)  local maximum at x = -4 (no local minimum) 
A)  local minimum at x = -4 (no local maximum) 
B)  local maximum at x = -4, local minimum at x = 4 
C)  no local maximum or minimum 
D)  local maximum at x = -4 (no local minimum)

Question 6

Solve the problem.
-A backpack manufacturer is planning to expand its work force. They estimate that the number of backpacks
produced by hiring new workers is given by   Determine when the rate of
backpacks is increasing and when it is decreasing. Determine the point of diminishing returns and the
maximum rate of change of backpack production.

Accepted Answer

The rate of change of backpack productio

Question 7

Provide an appropriate response.
-Use the first derivative test to determine the local extrema, if any, for the function:

Accepted Answer

A)  local min at x = 2 
B)  local max at x = - 4 and local min at x = 2 
C)  local max at x = 2 and local min at - 4 
D)  local max at x = - 4 
A)  local min at x = 2 
B)  local max at x = - 4 and local min at x = 2 
C)  local max at x = 2 and local min at - 4 
D)  local max at x = - 4

Question 8

Provide an appropriate response.
-Use a graphing utility to approximate where the local extrema of the function   are to two decimal places.

Accepted Answer

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

Question 9

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave downward

Accepted Answer

A)    
B)  (-5, 2); x = 0 
C)  (-5, 5); no inflection points 
D)    
A)    
B)  (-5, 2); x = 0 
C)  (-5, 5); no inflection points 
D)

Question 10

Solve the problem.
-The percent of concentration of a certain drug in the bloodstream x hr after the drug is administered is given by   How long after the drug has been administered is the concentration a maximum? Round answer to the nearest tenth, if necessary.

Accepted Answer

A)  7 hr 
B)  2 hr 
C)  2.5 hr 
D)  4.9 hr 
A)  7 hr 
B)  2 hr 
C)  2.5 hr 
D)  4.9 hr

Question 11

Solve the problem.
-The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d), in feet, was approximated by the function   Find the relative maximum of the function.

Accepted Answer

A)  (0, 6.9) 
B)  (175, 61.25) 
C)  (350, 129.4) 
D)  (175, 68.15) 
A)  (0, 6.9) 
B)  (175, 61.25) 
C)  (350, 129.4) 
D)  (175, 68.15)

Question 12

Provide an appropriate response.
-Identify the intervals where f(x) is decreasing.

Accepted Answer

The answer of Provide an appropriate response.
-Identify the intervals where...

Question 13

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points.
-Concave upward

Accepted Answer

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

Question 14

Provide an appropriate response.
-A drug that stimulates reproduction is introduced into a colony of bacteria. After t minutes, the number of bacteria is given approximately by:   At what value of t is the number of bacteria a maximum?

Accepted Answer

A)  24 min 
B)  12 min 
C)  6 min 
D)  30 min 
A)  24 min 
B)  12 min 
C)  6 min 
D)  30 min

Question 15

Sketch a graph of a single function that has these properties.
-

Accepted Answer

A)  Domain: All real numbers except -9; y intercept: 0; x intercept: 0 
B)    y intercept: 0; x intercept: 0 
C)  Domain: All real numbers except 9; y intercept: 0; x intercept: 0 
D)  Domain: All real numbers except -9; y intercept: 0; no x intercept 
A)  Domain: All real numbers except -9; y intercept: 0; x intercept: 0 
B)    y intercept: 0; x intercept: 0 
C)  Domain: All real numbers except 9; y intercept: 0; x intercept: 0 
D)  Domain: All real numbers except -9; y intercept: 0; no x intercept

Question 16

Sketch a graph of a single function that has these properties.
-Find

Accepted Answer

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

Question 17

Sketch a graph of a single function that has these properties.
-Find the inflection point(s) for

Accepted Answer

A)    
B)  (0, 6) and (2, 2) 
C)  (0, 0) 
D)  (0, 0) and (2, 2) 
A)    
B)  (0, 6) and (2, 2) 
C)  (0, 0) 
D)  (0, 0) and (2, 2)

Question 18

Sketch the graph and show all local extrema and inflection points.
-

Accepted Answer

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

Question 19

Solve the problem.
-The annual revenue and cost functions for a manufacturer of zip drives are approximately   and C(x) = 160x + 100,000, where x denotes the number of drives made. What is the maximum annual profit?

Accepted Answer

A)  $1,620,000 
B)  $1,820,000 
C)  $1,720,000 
D)  $1,520,000 
A)  $1,620,000 
B)  $1,820,000 
C)  $1,720,000 
D)  $1,520,000

Question 20

Sketch the graph and show all local extrema and inflection points.
-

Accepted Answer

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

Sketch a graph of a single function that has these properties. -Find

Provide an appropriate response. -Use a graphing utility to approximate the intervals where f(x) is decreasing and intervals where f(x) is increasing for the function Round your answer to two decimal places.

Find the limit, if it exists. -Find .

Find the limit, if it exists. -

Provide an appropriate response. -Given find the values of x corresponding to local maxima and local minima.

Provide an appropriate response. -Use the first derivative test to determine the local extrema, if any, for the function:

Provide an appropriate response. -Use a graphing utility to approximate where the local extrema of the function are to two decimal places.

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave downward

Solve the problem. -The percent of concentration of a certain drug in the bloodstream x hr after the drug is administered is given by How long after the drug has been administered is the concentration a maximum? Round answer to the nearest tenth, if necessary.

Solve the problem. -The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d), in feet, was approximated by the function Find the relative maximum of the function.

Provide an appropriate response. -Identify the intervals where f(x) is decreasing.

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave upward

Provide an appropriate response. -A drug that stimulates reproduction is introduced into a colony of bacteria. After t minutes, the number of bacteria is given approximately by: At what value of t is the number of bacteria a maximum?

Sketch a graph of a single function that has these properties. -

Sketch a graph of a single function that has these properties. -Find

Sketch a graph of a single function that has these properties. -Find the inflection point(s) for

Sketch the graph and show all local extrema and inflection points. -

Solve the problem. -The annual revenue and cost functions for a manufacturer of zip drives are approximately and C(x) = 160x + 100,000, where x denotes the number of drives made. What is the maximum annual profit?

Sketch the graph and show all local extrema and inflection points. -

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters

Exam 4: Graphing and Optimization

Sketch a graph of a single function that has these properties. -Find

Provide an appropriate response. -Use a graphing utility to approximate the intervals where f(x) is decreasing and intervals where f(x) is increasing for the function Round your answer to two decimal places.

Find the limit, if it exists. -Find .

Find the limit, if it exists. -

Provide an appropriate response. -Given find the values of x corresponding to local maxima and local minima.

Provide an appropriate response. -Use the first derivative test to determine the local extrema, if any, for the function:

Provide an appropriate response. -Use a graphing utility to approximate where the local extrema of the function are to two decimal places.

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave downward

Solve the problem. -The percent of concentration of a certain drug in the bloodstream x hr after the drug is administered is given by How long after the drug has been administered is the concentration a maximum? Round answer to the nearest tenth, if necessary.

Solve the problem. -The Olympic flame at the 1992 Summer Olympics was lit by a flaming arrow. As the arrow moved d feet horizontally from the archer, assume that its height h(d), in feet, was approximated by the function Find the relative maximum of the function.

Provide an appropriate response. -Identify the intervals where f(x) is decreasing.

Find the intervals where the function has the indicated concavity. Give the x coordinates of inflection points. -Concave upward

Provide an appropriate response. -A drug that stimulates reproduction is introduced into a colony of bacteria. After t minutes, the number of bacteria is given approximately by: At what value of t is the number of bacteria a maximum?

Sketch a graph of a single function that has these properties. -

Sketch a graph of a single function that has these properties. -Find

Sketch a graph of a single function that has these properties. -Find the inflection point(s) for

Sketch the graph and show all local extrema and inflection points. -

Solve the problem. -The annual revenue and cost functions for a manufacturer of zip drives are approximately and C(x) = 160x + 100,000, where x denotes the number of drives made. What is the maximum annual profit?

Sketch the graph and show all local extrema and inflection points. -

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Integration

Additional Integration Topics

Multivariable Calculus

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters