Question 1

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

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

Question 2

If   . ​

Accepted Answer

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

Question 3

Find the indicated derivative. Find   .
​

Accepted Answer

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

Question 4

The total revenue function (in dollars) for a blender is   , where x is the number of units sold. What is the average rate of change in revenue R(x) as x increases from 20 to 30 units? ​

Accepted Answer

A)  $254.60 per unit 
B)  $59.80 per unit 
C)  $48.20 per unit 
D)  $49.80 per unit 
E)  $49.00 per unit 
A)  $254.60 per unit 
B)  $59.80 per unit 
C)  $48.20 per unit 
D)  $49.80 per unit 
E)  $49.00 per unit

Question 5

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

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

Question 6

For the function in this problem, approximate   near   by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places. ​   ​

Accepted Answer

A)  -0.1641 
B)  -0.1698 
C)  -0.5411 
D)  -0.5102 
E)  -0.3735 
A)  -0.1641 
B)  -0.1698 
C)  -0.5411 
D)  -0.5102 
E)  -0.3735

Question 7

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

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

Question 8

Find the derivative of the equation   , but do not simplify your answer. ​

Accepted Answer

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

Question 9

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

Accepted Answer

A)  3 
B)  0 
C)  4 
D)  1 
E)  does not exist 
A)  3 
B)  0 
C)  4 
D)  1 
E)  does not exist

Question 10

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

Accepted Answer

A)  -6 
B)  -7 
C)  3 
D)  -5 
E)  does not exist 
A)  -6 
B)  -7 
C)  3 
D)  -5 
E)  does not exist

Question 11

Differentiate the given function. ​   ​

Accepted Answer

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

Question 12

Suppose that for selected years from 1970 to 2006, the following table shows the percent of total U.S. workers who are female. ​
 
​
Assume these data can be modeled with the function   where p(t) is the percent of the U.S. workforce that is female and t is the number of years past 1970. Find the instantaneous rate of change in 2000 and 2006 by using the function that models the instantaneous rate of change of the percent of U.S. workers who are female. Round your answer to three decimal places.
​

Accepted Answer

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

Question 13

Suppose the lowest temperature recorded in Indianapolis, Indiana, was   If x is the wind speed in miles per hour and   , then the wind chill (in degrees Fahrenheit) for an air temperature of   can be approximated by the function   . At what rate is the wind chill changing when the wind speed is 50 mph? Round your answer to two decimal places.

Accepted Answer

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

Question 14

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 15

For the function in this problem, approximate   by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places. ​   ​

Accepted Answer

A)  -0.298 
B)  ​-0.421 
C)  -0.544 
D)  -0.187 
E)  -0.655 
A)  -0.298 
B)  ​-0.421 
C)  -0.544 
D)  -0.187 
E)  -0.655

Question 16

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 17

Find the derivative at the given x-value with the appropriate rule. ​   ​

Accepted Answer

A)  -9 
B)  -32 
C)  0 
D)  -4.5 
E)  9 
A)  -9 
B)  -32 
C)  0 
D)  -4.5 
E)  9

Question 18

The graph of a company's total cost function is shown. Will the 201st item or the 501st item cost more to produce? ​   ​

Accepted Answer

A)  201st 
B)  501st 
A)  201st 
B)  501st

Question 19

Find the coordinates of points where the graph of   has horizontal tangents. As a check, graph   and see whether the points you found look as though they have horizontal tangents.   ​

Accepted Answer

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

Question 20

If   and   , find   . ​

Accepted Answer

A)  20 
B)  6 
C)  -2 
D)  -14 
E)  does not exist 
A)  20 
B)  6 
C)  -2 
D)  -14 
E)  does not exist

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

If .

Find the indicated derivative. Find .

The total revenue function (in dollars) for a blender is , where x is the number of units sold. What is the average rate of change in revenue R(x) as x increases from 20 to 30 units?

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

For the function in this problem, approximate near by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places.

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Find the derivative of the equation , but do not simplify your answer.

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

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

Differentiate the given function.

Find the derivative of the function.

For the function in this problem, approximate by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places.

Find the derivative at the given x-value with the appropriate rule.

The graph of a company's total cost function is shown. Will the 201st item or the 501st item cost more to produce?

Find the coordinates of points where the graph of has horizontal tangents. As a check, graph and see whether the points you found look as though they have horizontal tangents.

If and , find .

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

Exam 9: Derivatives

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

If . ​

Find the indicated derivative. Find . ​

The total revenue function (in dollars) for a blender is , where x is the number of units sold. What is the average rate of change in revenue R(x) as x increases from 20 to 30 units? ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

For the function in this problem, approximate near by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places. ​ ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

Find the derivative of the equation , but do not simplify your answer. ​

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

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

Differentiate the given function. ​ ​

Find the derivative of the function. ​ ​

For the function in this problem, approximate by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places. ​ ​

Find the derivative at the given x-value with the appropriate rule. ​ ​

The graph of a company's total cost function is shown. Will the 201st item or the 501st item cost more to produce? ​ ​

Find the coordinates of points where the graph of has horizontal tangents. As a check, graph and see whether the points you found look as though they have horizontal tangents. ​

If and , find . ​

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

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

If .

Find the indicated derivative. Find .

The total revenue function (in dollars) for a blender is , where x is the number of units sold. What is the average rate of change in revenue R(x) as x increases from 20 to 30 units?

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

For the function in this problem, approximate near by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places.

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Find the derivative of the equation , but do not simplify your answer.

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

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

Differentiate the given function.

Find the derivative of the function.

For the function in this problem, approximate by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places.

Find the derivative at the given x-value with the appropriate rule.

The graph of a company's total cost function is shown. Will the 201st item or the 501st item cost more to produce?

Find the coordinates of points where the graph of has horizontal tangents. As a check, graph and see whether the points you found look as though they have horizontal tangents.

If and , find .