Question 1

Suppose that the demand function for q units of an appliance priced at $p per unit is given by   find the rate of change of price with respect to the number of appliances. ​

Accepted Answer

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

Question 2

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 3

Find all x-values for which the slope of the tangent is 0 for the given function. ​   ​

Accepted Answer

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

Question 4

Ballistics experts are able to identify the weapon that fired a certain bullet by studying the markings on the bullet. Tests are conducted by firing into a bale of paper. Suppose the distance s, in inches, that the bullet travels into the paper is given by   for   second, find the velocity of the bullet one-tenth of a second after it hits the paper. Round your answer to two decimal places. ​

Accepted Answer

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

Question 5

Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by   . Find   , if it exists. ​

Accepted Answer

A)  $0 
B)  $13 
C)  $117 
D)  $1,300 
E)  does not exist 
A)  $0 
B)  $13 
C)  $117 
D)  $1,300 
E)  does not exist

Question 6

Find all points (x, y) where the slope of the tangent is 0 for the given function. ​   ​

Accepted Answer

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

Question 7

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility. ​   ​

Accepted Answer

A)  -2 
B)  -4 
C)  -31 
D)  4 
E)  0 
A)  -2 
B)  -4 
C)  -31 
D)  4 
E)  0

Question 8

The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by   . Find the percent of the pollution that could be removed if spending C were allowed to increase without bound. ​

Accepted Answer

A)  1,700% 
B)  17,000% 
C)  0% 
D)  200% 
E)  100% 
A)  1,700% 
B)  17,000% 
C)  0% 
D)  200% 
E)  100%

Question 9

For the function given, find all x-values where the graph of   is falling. ​   ​

Accepted Answer

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

Question 10

Use analytic methods to find any point of discontinuity for the given function. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  continuous everywhere 
A)    
B)    
C)    
D)    
E)  continuous everywhere

Question 11

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 12

For the function given, find all x-values where f (x) has a local maximum point. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  no such x-values exist 
A)    
B)    
C)    
D)    
E)  no such x-values exist

Question 13

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​   ​

Accepted Answer

A)    
B)  18 
C)    
D)  0 
E)  does not exist 
A)    
B)  18 
C)    
D)  0 
E)  does not exist

Question 14

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places. ​   ​

Accepted Answer

A)  -0.292 
B)  0.583 
C)  -0.194 
D)  -1.750 
E)  1.750 
A)  -0.292 
B)  0.583 
C)  -0.194 
D)  -1.750 
E)  1.750

Question 15

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

Question 16

Use analytic methods to find the limit as   for the given function. ​   ​

Accepted Answer

A)  920 
B)  240 
C)  -920 
D)  -240 
E)  does not exist 
A)  920 
B)  240 
C)  -920 
D)  -240 
E)  does not exist

Question 17

If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by ​   ,
​
Find the rate of change of C with respect to p.

Accepted Answer

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

Question 18

For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value. ​   ​   ​

Accepted Answer

A)  discontinuous 
B)  continuous 
A)  discontinuous 
B)  continuous

Question 19

If the national consumption function is given by   find the marginal propensity to consume,   . ​

Accepted Answer

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

Question 20

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by   , where t is the number of days on the job. What is the domain for this application? ​

Accepted Answer

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

Suppose that the demand function for q units of an appliance priced at $p per unit is given by find the rate of change of price with respect to the number of appliances.

Find all x-values for which the slope of the tangent is 0 for the given function.

Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by . Find , if it exists.

Find all points (x, y) where the slope of the tangent is 0 for the given function.

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility.

The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by . Find the percent of the pollution that could be removed if spending C were allowed to increase without bound.

For the function given, find all x-values where the graph of is falling.

Use analytic methods to find any point of discontinuity for the given function.

Find the derivative of the function.

For the function given, find all x-values where f (x) has a local maximum point.

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places.

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 analytic methods to find the limit as for the given function.

If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by , Find the rate of change of C with respect to p.

For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value.

If the national consumption function is given by find the marginal propensity to consume, .

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application?

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

Suppose that the demand function for q units of an appliance priced at $p per unit is given by find the rate of change of price with respect to the number of appliances. ​

Find all x-values for which the slope of the tangent is 0 for the given function. ​ ​

Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by . Find , if it exists. ​

Find all points (x, y) where the slope of the tangent is 0 for the given function. ​ ​

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility. ​ ​

The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by . Find the percent of the pollution that could be removed if spending C were allowed to increase without bound. ​

For the function given, find all x-values where the graph of is falling. ​ ​

Use analytic methods to find any point of discontinuity for the given function. ​ ​

Find the derivative of the function. ​ ​

For the function given, find all x-values where f (x) has a local maximum point. ​ ​

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. ​ ​

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places. ​ ​

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 analytic methods to find the limit as for the given function. ​ ​

If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by ​ , ​ Find the rate of change of C with respect to p.

For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value. ​ ​ ​

If the national consumption function is given by find the marginal propensity to consume, . ​

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application? ​

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

Suppose that the demand function for q units of an appliance priced at $p per unit is given by find the rate of change of price with respect to the number of appliances.

Find all x-values for which the slope of the tangent is 0 for the given function.

Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by . Find , if it exists.

Find all points (x, y) where the slope of the tangent is 0 for the given function.

Find the derivative at the given x-value with the numerical derivative feature of a graphing utility.

The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by . Find the percent of the pollution that could be removed if spending C were allowed to increase without bound.

For the function given, find all x-values where the graph of is falling.

Use analytic methods to find any point of discontinuity for the given function.

Find the derivative of the function.

For the function given, find all x-values where f (x) has a local maximum point.

Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.

Use the numerical derivative feature of a graphing utility to find the derivative of the function at the given x-value. Round your answer to three decimal places.

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 analytic methods to find the limit as for the given function.

If the cost C (in dollars) of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by , Find the rate of change of C with respect to p.

For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value.

If the national consumption function is given by find the marginal propensity to consume, .

Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application?