Question 1

A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist, where   . Confirm your results analytically. ​   ​   ​

Accepted Answer

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

Question 2

Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces of equipment used, according to   ,   , where x is the number of pieces of equipment used. Using how many pieces of equipment will minimize the cost? ​​

Accepted Answer

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

Question 3

In this problem,   and its graph are given. Use the graph of   to determine where   is concave up.

Accepted Answer

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

Question 4

A function and its graph are given. Use the second derivative to locate all x-values of points of inflection on the graph of   . Check these results against the graph shown.

Accepted Answer

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

Question 5

If the total revenue function for a blender is   , determine how many units x must be sold to provide the maximum total revenue in dollars. ​​

Accepted Answer

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

Question 6

Both a function and its derivative are given. Use them to find intervals on which the function is decreasing. ​     ​

Accepted Answer

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

Question 7

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 8

A function and its graph are given. Use the second derivative to determine intervals on which the function is concave up. Check these results against the graph shown. ​   ​   ​

Accepted Answer

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

Question 9

A function and its graph are given. From the graph estimate where   has a relative maximum. ​     ​

Accepted Answer

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

Question 10

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) ​

Question 11

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 12

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by   ,   . Find the maximum value of x. Round your answer to two decimal places. ​​

Accepted Answer

A) 2.83 mg 
B) 530.33 mg 
C) 1166.73 mg 
D) 8.77 mg 
E) 1125.30 mg 
A) 2.83 mg 
B) 530.33 mg 
C) 1166.73 mg 
D) 8.77 mg 
E) 1125.30 mg

A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist, where . Confirm your results analytically.

Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces of equipment used, according to , , where x is the number of pieces of equipment used. Using how many pieces of equipment will minimize the cost?

In this problem, and its graph are given. Use the graph of to determine where is concave up.

A function and its graph are given. Use the second derivative to locate all x-values of points of inflection on the graph of . Check these results against the graph shown.

If the total revenue function for a blender is , determine how many units x must be sold to provide the maximum total revenue in dollars.

Both a function and its derivative are given. Use them to find intervals on which the function is decreasing.

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

A function and its graph are given. Use the second derivative to determine intervals on which the function is concave up. Check these results against the graph shown.

A function and its graph are given. From the graph estimate where has a relative maximum.

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: )

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

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . Find the maximum value of x. Round your answer to two decimal places.

Algebraic Concepts

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; Data Description

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 11: Applications of Derivatives

A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist, where . Confirm your results analytically. ​ ​ ​

Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces of equipment used, according to , , where x is the number of pieces of equipment used. Using how many pieces of equipment will minimize the cost? ​​

In this problem, and its graph are given. Use the graph of to determine where is concave up.

A function and its graph are given. Use the second derivative to locate all x-values of points of inflection on the graph of . Check these results against the graph shown.

If the total revenue function for a blender is , determine how many units x must be sold to provide the maximum total revenue in dollars. ​​

Both a function and its derivative are given. Use them to find intervals on which the function is decreasing. ​ ​

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

A function and its graph are given. Use the second derivative to determine intervals on which the function is concave up. Check these results against the graph shown. ​ ​ ​

A function and its graph are given. From the graph estimate where has a relative maximum. ​ ​

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: ) ​​

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

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . Find the maximum value of x. Round your answer to two decimal places. ​​

Algebraic Concepts

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; Data Description

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist, where . Confirm your results analytically.

Suppose that the monthly cost in dollars of mining a certain ore is related to the number of pieces of equipment used, according to , , where x is the number of pieces of equipment used. Using how many pieces of equipment will minimize the cost?

If the total revenue function for a blender is , determine how many units x must be sold to provide the maximum total revenue in dollars.

Both a function and its derivative are given. Use them to find intervals on which the function is decreasing.

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

A function and its graph are given. Use the second derivative to determine intervals on which the function is concave up. Check these results against the graph shown.

A function and its graph are given. From the graph estimate where has a relative maximum.

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: )

The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by , . Find the maximum value of x. Round your answer to two decimal places.