Question 1

Sketch a graph of the function.
-

Accepted Answer

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

Question 2

Find the limit, if it exists.
-Find

Accepted Answer

A)    
B)  0 
C)    
D)  1 
A)    
B)  0 
C)    
D)  1

Question 3

Provide an appropriate response.
-Find the critical values and determine the intervals where f(x) is decreasing for f(x) = 3(x - 4)2/3 + 6.

Accepted Answer

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

Question 4

Provide an appropriate response.
-Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Accepted Answer

A)    
B)    
C)  Relative minimum: (0, 5) 
D)  Relative maximum: (0, 5) 
A)    
B)    
C)  Relative minimum: (0, 5) 
D)  Relative maximum: (0, 5)

Question 5

Solve the problem.
-A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. Round to
The nearest tenth, if necessary.

Accepted Answer

A)  7.2 ft 
B)  3.6 ft 
C)  3.2 ft 
D)  6.4 ft 
A)  7.2 ft 
B)  3.6 ft 
C)  3.2 ft 
D)  6.4 ft

Question 6

Provide an appropriate response.
-The total cost, in dollars, of producing x cell phones is approximated by the function   Find the minimum average cost.

Accepted Answer

A)  The minimum average cost is $75 when x = 875 cell phones. 
B)  The minimum average cost is $875 when x = 75 cell phones. 
C)  The minimum average cost is $74 when x = 20 cell phones. 
D)  The minimum average cost is $10 when x = 100 cell phones. 
A)  The minimum average cost is $75 when x = 875 cell phones. 
B)  The minimum average cost is $875 when x = 75 cell phones. 
C)  The minimum average cost is $74 when x = 20 cell phones. 
D)  The minimum average cost is $10 when x = 100 cell phones.

Question 7

Sketch a graph of a single function that has these properties.
-f(x) = 4x + 8

Accepted Answer

A)    y intercept: 8; x intercept: -2 
B)    y intercept: -2; x intercept: 8 
C)    y intercept: 8; x intercept: -2 
D)    y intercept: 8; x intercept: 2 
A)    y intercept: 8; x intercept: -2 
B)    y intercept: -2; x intercept: 8 
C)    y intercept: 8; x intercept: -2 
D)    y intercept: 8; x intercept: 2

Question 8

Solve the problem.
-The average manufacturing cost per unit (in hundreds of dollars) for producing x units of a product is given by:   At what production level will the average cost per unit be maximum?

Accepted Answer

A)  652 units 
B)  12 units 
C)  5 units 
D)  1 unit 
A)  652 units 
B)  12 units 
C)  5 units 
D)  1 unit

Question 9

Solve the problem.
-A computer software company sells 20,000 copies of a certain computer game each year. It costs the company $1.00 to store each copy of the game for one year. Each time it must produce additional copies, it costs the
Company $625 to set up production. How many copies of the game should the company produce during each
Production run in order to minimize its total storage and set-up costs?

Accepted Answer

A)  5000 copies in 4 production runs 
B)  20,000 copies in 1 production run 
C)  10,000 copies in 2 production runs 
D)  4000 copies in 5 production runs 
A)  5000 copies in 4 production runs 
B)  20,000 copies in 1 production run 
C)  10,000 copies in 2 production runs 
D)  4000 copies in 5 production runs

Question 10

Solve the problem.
-A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 102 in. What dimensions will give a box with a square end the largest
Possible volume?

Accepted Answer

A)  17 in. × 34 in. × 34 in. 
B)  34 in. × 34 in. × 34 in. 
C)  17 in. × 17 in. × 34 in. 
D)  17 in. × 17 in. × 85 in. 
A)  17 in. × 34 in. × 34 in. 
B)  34 in. × 34 in. × 34 in. 
C)  17 in. × 17 in. × 34 in. 
D)  17 in. × 17 in. × 85 in.

Question 11

Provide an appropriate response.
-Identify the intervals where f‛(x) > 0.

Accepted Answer

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

Question 12

Find the limit, if it exists.
-Find:

Accepted Answer

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

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

Sketch a graph of the function.
-

Accepted Answer

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

Question 15

Provide an appropriate response.
-

Accepted Answer

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

Question 16

Find the intervals where f''(x)  0 as indicated.
-

Accepted Answer

A)  (-5, 2) 
B)    
C)  (-5, 5) 
D)    
A)  (-5, 2) 
B)    
C)  (-5, 5) 
D)

Question 17

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

Accepted Answer

A)    y intercept: 8; x intercept: -64 
B)    y intercept: -64; x intercept: 8 
C)    y intercept: 8; x intercept: -64 
D)    y intercept: 8; x intercept: -64 
A)    y intercept: 8; x intercept: -64 
B)    y intercept: -64; x intercept: 8 
C)    y intercept: 8; x intercept: -64 
D)    y intercept: 8; x intercept: -64

Question 18

Provide an appropriate response.
-Sketch the graph of   Include sketch of all asymptotes.

Accepted Answer

The answer of Provide an appropriate response.
-Sketch the graph of...

Question 19

Provide an appropriate response.
-Write the sign chart that corresponds to the following graph of f(x):

Accepted Answer

The answer of Provide an appropriate response.
-Write the sign chart...

Question 20

Provide an appropriate response.
-The critical values of   are x = -2 and x = 2. Use the first derivative test to determine which of the critical values correspond to a local maximum.

Accepted Answer

A)  x = - 2 
B)  x = 2 
C)  x = 0 and x = 2 
D)  x = 2 and x = - 2 
A)  x = - 2 
B)  x = 2 
C)  x = 0 and x = 2 
D)  x = 2 and x = - 2

Sketch a graph of the function. -

Find the limit, if it exists. -Find

Provide an appropriate response. -Find the critical values and determine the intervals where f(x) is decreasing for f(x) = 3(x - 4)2/3 + 6.

Provide an appropriate response. -Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Solve the problem. -A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. Round to The nearest tenth, if necessary.

Provide an appropriate response. -The total cost, in dollars, of producing x cell phones is approximated by the function Find the minimum average cost.

Sketch a graph of a single function that has these properties. -f(x) = 4x + 8

Solve the problem. -The average manufacturing cost per unit (in hundreds of dollars) for producing x units of a product is given by: At what production level will the average cost per unit be maximum?

Solve the problem. -A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 102 in. What dimensions will give a box with a square end the largest Possible volume?

Provide an appropriate response. -Identify the intervals where f‛(x) > 0.

Find the limit, if it exists. -Find:

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

Sketch a graph of the function. -

Provide an appropriate response. -

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

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

Provide an appropriate response. -Sketch the graph of Include sketch of all asymptotes.

Provide an appropriate response. -Write the sign chart that corresponds to the following graph of f(x):

Provide an appropriate response. -The critical values of are x = -2 and x = 2. Use the first derivative test to determine which of the critical values correspond to a local maximum.

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 the function. -

Find the limit, if it exists. -Find

Provide an appropriate response. -Find the critical values and determine the intervals where f(x) is decreasing for f(x) = 3(x - 4)2/3 + 6.

Provide an appropriate response. -Find the relative extrema of the function. List your answer(s) in terms of ordered pair(s).

Solve the problem. -A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is twice as long as it is wide. Find the width of the box that can be produced using the minimum amount of material. Round to The nearest tenth, if necessary.

Provide an appropriate response. -The total cost, in dollars, of producing x cell phones is approximated by the function Find the minimum average cost.

Sketch a graph of a single function that has these properties. -f(x) = 4x + 8

Solve the problem. -The average manufacturing cost per unit (in hundreds of dollars) for producing x units of a product is given by: At what production level will the average cost per unit be maximum?

Solve the problem. -A private shipping company will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 102 in. What dimensions will give a box with a square end the largest Possible volume?

Provide an appropriate response. -Identify the intervals where f‛(x) > 0.

Find the limit, if it exists. -Find:

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

Sketch a graph of the function. -

Provide an appropriate response. -

Find the intervals where f''(x) < 0 ir f''(x) > 0 as indicated. -

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

Provide an appropriate response. -Sketch the graph of Include sketch of all asymptotes.

Provide an appropriate response. -Write the sign chart that corresponds to the following graph of f(x):

Provide an appropriate response. -The critical values of are x = -2 and x = 2. Use the first derivative test to determine which of the critical values correspond to a local maximum.

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