Question 1

Find the absolute maximum for   on the interval [a, b].   ,

Accepted Answer

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

Question 2

For the given function, find intervals of x-values where the function is increasing.

Accepted Answer

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

Question 3

For the given function, find

Accepted Answer

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

Question 4

A vacationer on an island 8 miles offshore from a point that is 48 miles from a town to which the vacationer must travel occasionally. (See the figure.) The vacationer has a boat capable of traveling 30 mph and can go by auto along the coast at 55 mph. At what distance x from the point on shore closest to the vacationer on the island should the boat be left to minimize the time it takes to get to town? Round your answer to one decimal place. ​   Where   ,   ​

Accepted Answer

A)  ​6.1 miles 
B)  ​5.2 miles 
C)  ​5.9 miles 
D)  ​3.8 miles 
E)  ​4.3 miles 
A)  ​6.1 miles 
B)  ​5.2 miles 
C)  ​5.9 miles 
D)  ​3.8 miles 
E)  ​4.3 miles

Question 5

The monthly demand function for x units of a product sold by a monopoly is   dollars per unit, and its average cost is   dollars. If production is limited to 111 units, find the number of units that maximizes profit. (​Note: ​   ) ​​

Accepted Answer

A)  40 units 
B)  111 units 
C)  107 units 
D)  11 units 
E)  54 units 
A)  40 units 
B)  111 units 
C)  107 units 
D)  11 units 
E)  54 units

Question 6

Suppose that a company needs 800 items during a year and that preparation for each production run costs $60. Suppose further that it costs $8 to produce each item and $0.45 to store an item for one year. Use the inventory cost model to find the number of items in each production run that will minimize the total costs of production and storage. ​

Accepted Answer

A)  449 items 
B)  462 items 
C)  491 items 
D)  480 items 
E)  469 items 
A)  449 items 
B)  462 items 
C)  491 items 
D)  480 items 
E)  469 items

Question 7

Make a sign diagram for the function and determine all x-values at which relative maxima occur. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  no relative maxima 
A)    
B)    
C)    
D)    
E)  no relative maxima

Question 8

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by   . Find C values for which p is increasing. ​

Accepted Answer

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

Question 9

Use the indicated x-values on the graph of   to determine intervals over which the graph is concave up.   ​

Accepted Answer

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

Question 10

Find all vertical asymptotes for the given function.

Accepted Answer

A)    
B)    
C)    
D)    
E)  no vertical asymptotes 
A)    
B)    
C)    
D)    
E)  no vertical asymptotes

Question 11

Find all relative minima of the given function.

Accepted Answer

A)    
B)    
C)    
D)    
E)  no relative minima 
A)    
B)    
C)    
D)    
E)  no relative minima

Question 12

Find the x-value at which the absolute maximum of f (x) occurs on the interval [a, b].   ,

Accepted Answer

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

Question 13

For the given function, use the graph to identify the x-value for which   . You may use the derivative to check your conclusion. ​   ​   ​

Accepted Answer

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

Question 14

If the total revenue function for a blender is   , find the maximum revenue if production is limited to at most 200 blenders. ​

Accepted Answer

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

Question 15

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by   ,   . For what t-values is x increasing? Round answers to two decimal places. ​

Accepted Answer

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

Question 16

For the given function, use the graph to identify x-values for which   . You may use the derivative to check your conclusion. ​   ​​

Accepted Answer

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

Question 17

If the total revenue function for a blender is   , find the maximum revenue. ​

Accepted Answer

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

Question 18

Find any horizontal asymptotes for the given function.

Accepted Answer

A)    
B)    
C)    
D)    
E)  no horizontal asymptotes 
A)    
B)    
C)    
D)    
E)  no horizontal asymptotes

Question 19

Both a function and its derivative are given. Use them to find all critical points.

Accepted Answer

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

Question 20

A small business has weekly average costs (in dollars) of   , where x is the number of units produced each week. The competitive market price for this business's product is $62 per unit. If production is limited to 430 units per week, find the maximum profit. (​Note:   ) ​​

Accepted Answer

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

Find the absolute maximum for on the interval [a, b]. ,

For the given function, find intervals of x-values where the function is increasing.

For the given function, find

The monthly demand function for x units of a product sold by a monopoly is dollars per unit, and its average cost is dollars. If production is limited to 111 units, find the number of units that maximizes profit. (Note: )

Make a sign diagram for the function and determine all x-values at which relative maxima occur.

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find C values for which p is increasing.

Use the indicated x-values on the graph of to determine intervals over which the graph is concave up.

Find all vertical asymptotes for the given function.

Find all relative minima of the given function.

Find the x-value at which the absolute maximum of f (x) occurs on the interval [a, b]. ,

For the given function, use the graph to identify the x-value for which . You may use the derivative to check your conclusion.

If the total revenue function for a blender is , find the maximum revenue if production is limited to at most 200 blenders.

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . For what t-values is x increasing? Round answers to two decimal places.

For the given function, use the graph to identify x-values for which . You may use the derivative to check your conclusion.

If the total revenue function for a blender is , find the maximum revenue.

Find any horizontal asymptotes for the given function.

Both a function and its derivative are given. Use them to find all critical points.

A small business has weekly average costs (in dollars) of , where x is the number of units produced each week. The competitive market price for this business's product is $62 per unit. If production is limited to 430 units per week, find the maximum profit. (Note: )

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

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Exam 10: Derivatives

Find the absolute maximum for on the interval [a, b]. ,

For the given function, find intervals of x-values where the function is increasing.

For the given function, find

The monthly demand function for x units of a product sold by a monopoly is dollars per unit, and its average cost is dollars. If production is limited to 111 units, find the number of units that maximizes profit. (​Note: ​ ) ​​

Make a sign diagram for the function and determine all x-values at which relative maxima occur. ​ ​

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find C values for which p is increasing. ​

Use the indicated x-values on the graph of to determine intervals over which the graph is concave up. ​

Find all vertical asymptotes for the given function.

Find all relative minima of the given function.

Find the x-value at which the absolute maximum of f (x) occurs on the interval [a, b]. ,

For the given function, use the graph to identify the x-value for which . You may use the derivative to check your conclusion. ​ ​ ​

If the total revenue function for a blender is , find the maximum revenue if production is limited to at most 200 blenders. ​

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . For what t-values is x increasing? Round answers to two decimal places. ​

For the given function, use the graph to identify x-values for which . You may use the derivative to check your conclusion. ​ ​​

If the total revenue function for a blender is , find the maximum revenue. ​

Find any horizontal asymptotes for the given function.

Both a function and its derivative are given. Use them to find all critical points.

A small business has weekly average costs (in dollars) of , where x is the number of units produced each week. The competitive market price for this business's product is $62 per unit. If production is limited to 430 units per week, find the maximum profit. (​Note: ) ​​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

The monthly demand function for x units of a product sold by a monopoly is dollars per unit, and its average cost is dollars. If production is limited to 111 units, find the number of units that maximizes profit. (Note: )

Make a sign diagram for the function and determine all x-values at which relative maxima occur.

The percent p of impurities that can be removed from the waste water of a manufacturing process at a cost of C dollars is given by . Find C values for which p is increasing.

Use the indicated x-values on the graph of to determine intervals over which the graph is concave up.

For the given function, use the graph to identify the x-value for which . You may use the derivative to check your conclusion.

If the total revenue function for a blender is , find the maximum revenue if production is limited to at most 200 blenders.

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . For what t-values is x increasing? Round answers to two decimal places.

For the given function, use the graph to identify x-values for which . You may use the derivative to check your conclusion.

If the total revenue function for a blender is , find the maximum revenue.

A small business has weekly average costs (in dollars) of , where x is the number of units produced each week. The competitive market price for this business's product is $62 per unit. If production is limited to 430 units per week, find the maximum profit. (Note: )