Question 1

Differentiate the given function. ​   ​

Accepted Answer

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

Question 2

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. ​   ​

Accepted Answer

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

Question 3

Find the indicated derivative. Find   .
​

Accepted Answer

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

Question 4

For the given function, find the instantaneous rate of change at   . ​   ​

Accepted Answer

A) 20 
B) -20 
C) 1030 
D) -952 
E) does not exist 
A) 20 
B) -20 
C) 1030 
D) -952 
E) does not exist

Question 5

Write the equation of the line tangent to the graph of the given function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. ​   ​

Accepted Answer

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

Question 6

In the figure given in this problem, at points B and E draw an approximate tangent line and then use it to answer the following question. Is   greater at point B or at point E? ​   ​

Accepted Answer

A) point B 
B) point E 
A) point B 
B) point E

Question 7

For the function given, find all x-values where   . ​   ​

Accepted Answer

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

Question 8

The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by   where t is the number of weeks the campaign runs. What is the rate of change of sales at   ? Round your answer to five decimal places. ​

Accepted Answer

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

Question 9

Identify x-values where   ,   , and   . ​   ​

Accepted Answer

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

Question 10

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 11

This problem contains a function and its graph, where   . Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically. ​   ​   ​

Accepted Answer

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

Question 12

The graphs of a company's total revenue function   and total cost function   are shown. The cost function is a linear function of the number of units sold. From the sale of the 51st item, 501st item, and 801st item, rank from smallest to largest the amount of profit received. ​   ​

Accepted Answer

A) 801st, 51st, 501st 
B) 501st, 801st, 51st 
C) 801st, 501st, 51st 
D) 51st, 801st, 501st 
E) 51st, 501st, 801st 
A) 801st, 51st, 501st 
B) 501st, 801st, 51st 
C) 801st, 501st, 51st 
D) 51st, 801st, 501st 
E) 51st, 501st, 801st

Question 13

The following table shows the numbers of U.S. cellular subscriberships (in millions) from 1985 to 2002. ​   Source: The CTIA Semi-Annual Wireless Industry Survey
Assume that the number of U.S. cellular subscriberships, in millions, can be modeled by the function   , where t is the number of years past 1980. Find the function that models the instantaneous rate of change of the U.S. cellular subscriberships.
​

Accepted Answer

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

Question 14

Use the graph of   and the given c-value to find   . ​   ​   ​

Accepted Answer

A)    
B) -8 
C) 3 
D) -1 
E) does not exist 
A)    
B) -8 
C) 3 
D) -1 
E) does not exist

Question 15

For the given function, find the slope of the tangent line at   . A graphing utility's numerical derivative feature may be used to check your work. ​   ​

Accepted Answer

A) 3 
B) 12 
C) 4 
D) 48 
E) 18 
A) 3 
B) 12 
C) 4 
D) 48 
E) 18

Question 16

The sales of a product S (in thousands of dollars) are given by   , where x is the advertising expenditure (in thousands of dollars). Find the rate of change of sales with respect to advertising expenditure. Use the second derivative to find how this rate is changing at   . Round your answer to two decimal places. ​

Accepted Answer

A) 0.89 
B) -0.03 
C) 0.00 
D) -0.89 
E) -0.02 
A) 0.89 
B) -0.03 
C) 0.00 
D) -0.89 
E) -0.02

Question 17

The daily sales S (in thousands of dollars) that are attributed to an advertising campaign are given by   where t is the number of weeks the campaign runs. Find the rate of change of sales at any time t and use the second derivative to find how this rate is changing at   . Round your answer to four decimal places, when applicable. ​

Accepted Answer

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

Question 18

Suppose that the total cost function, in dollars, for a certain commodity is given by   , where x is the number of units produced. The average cost is given by   for any level of production. Find the level of production where the instantaneous rate of change of the average cost equals zero. Round your answer to two decimal places. ​

Accepted Answer

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

Question 19

Find the indicated derivative. Find   ​

Accepted Answer

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

Question 20

A chain of auto service stations has found that its monthly sales volume y (in dollars) is related to the price p (in dollars) of an oil change according to   ,   . What is the rate of change of sales volume when the price is $40? Interpret your answer. Round your answer to the nearest dollar. ​

Accepted Answer

A) -6,708. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $6,708. 
B) -298. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $298. 
C) -298. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $298. 
D) -149. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $149. 
E) -149. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $149. 
A) -6,708. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $6,708. 
B) -298. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $298. 
C) -298. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $298. 
D) -149. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $149. 
E) -149. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $149.

Differentiate the given function.

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line.

Find the indicated derivative. Find .

For the given function, find the instantaneous rate of change at .

Write the equation of the line tangent to the graph of the given function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct.

In the figure given in this problem, at points B and E draw an approximate tangent line and then use it to answer the following question. Is greater at point B or at point E?

For the function given, find all x-values where .

The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by where t is the number of weeks the campaign runs. What is the rate of change of sales at ? Round your answer to five decimal places.

Identify x-values where , , and .

Find the derivative of the function.

This problem contains a function and its graph, where . Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically.

The graphs of a company's total revenue function and total cost function are shown. The cost function is a linear function of the number of units sold. From the sale of the 51st item, 501st item, and 801st item, rank from smallest to largest the amount of profit received.

Use the graph of and the given c-value to find .

For the given function, find the slope of the tangent line at . A graphing utility's numerical derivative feature may be used to check your work.

Find the indicated derivative. Find

A chain of auto service stations has found that its monthly sales volume y (in dollars) is related to the price p (in dollars) of an oil change according to , . What is the rate of change of sales volume when the price is $40? Interpret your answer. Round your answer to the nearest dollar.

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

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 10: Derivatives

Differentiate the given function. ​ ​

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. ​ ​

Find the indicated derivative. Find . ​

For the given function, find the instantaneous rate of change at . ​ ​

Write the equation of the line tangent to the graph of the given function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. ​ ​

In the figure given in this problem, at points B and E draw an approximate tangent line and then use it to answer the following question. Is greater at point B or at point E? ​ ​

For the function given, find all x-values where . ​ ​

The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by where t is the number of weeks the campaign runs. What is the rate of change of sales at ? Round your answer to five decimal places. ​

Identify x-values where , , and . ​ ​

Find the derivative of the function. ​ ​

This problem contains a function and its graph, where . Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically. ​ ​ ​

The graphs of a company's total revenue function and total cost function are shown. The cost function is a linear function of the number of units sold. From the sale of the 51st item, 501st item, and 801st item, rank from smallest to largest the amount of profit received. ​ ​

Use the graph of and the given c-value to find . ​ ​ ​

For the given function, find the slope of the tangent line at . A graphing utility's numerical derivative feature may be used to check your work. ​ ​

Find the indicated derivative. Find ​

A chain of auto service stations has found that its monthly sales volume y (in dollars) is related to the price p (in dollars) of an oil change according to , . What is the rate of change of sales volume when the price is $40? Interpret your answer. Round your answer to the nearest dollar. ​

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

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Differentiate the given function.

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line.

Find the indicated derivative. Find .

For the given function, find the instantaneous rate of change at .

Write the equation of the line tangent to the graph of the given function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct.

In the figure given in this problem, at points B and E draw an approximate tangent line and then use it to answer the following question. Is greater at point B or at point E?

For the function given, find all x-values where .

The daily sales S (in thousands of dollars) attributed to an advertising campaign are given by where t is the number of weeks the campaign runs. What is the rate of change of sales at ? Round your answer to five decimal places.

Identify x-values where , , and .

Find the derivative of the function.

This problem contains a function and its graph, where . Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically.

The graphs of a company's total revenue function and total cost function are shown. The cost function is a linear function of the number of units sold. From the sale of the 51st item, 501st item, and 801st item, rank from smallest to largest the amount of profit received.

Use the graph of and the given c-value to find .

For the given function, find the slope of the tangent line at . A graphing utility's numerical derivative feature may be used to check your work.

Find the indicated derivative. Find

A chain of auto service stations has found that its monthly sales volume y (in dollars) is related to the price p (in dollars) of an oil change according to , . What is the rate of change of sales volume when the price is $40? Interpret your answer. Round your answer to the nearest dollar.