Question 1

Determine whether the function is continuous or discontinuous at the given x-value. ​   ​

Accepted Answer

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

Question 2

Find   and simplify. ​

Accepted Answer

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

Question 3

Use properties of limits and algebraic methods to find the limit, if it exists. ​   ​

Accepted Answer

A)  ​   
B)    
C)    
D)    
E)  does not exist 
A)  ​   
B)    
C)    
D)    
E)  does not exist

Question 4

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 5

Write the equation of the tangent line to each curve at the indicated point. As a check, graph both the function and the tangent line. ​   ​

Accepted Answer

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

Question 6

A graph of   is shown and a c-value is given. For this problem, use the graph to find   . ​     ​

Accepted Answer

A)  0 
B)  5 
C)  -5 
D)  -6 
E)  does not exist 
A)  0 
B)  5 
C)  -5 
D)  -6 
E)  does not exist

Question 7

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. ​   ​

Accepted Answer

A)  limit = 0, vertical asymptote 
B)  limit = 0, horizontal asymptote 
C)  limit = 2, horizontal asymptote 
D)  limit = 2, vertical asymptote 
E)  does not exist 
A)  limit = 0, vertical asymptote 
B)  limit = 0, horizontal asymptote 
C)  limit = 2, horizontal asymptote 
D)  limit = 2, vertical asymptote 
E)  does not exist

Question 8

The revenue (in thousands of dollars) from the sale of a product is   , where x is the number of units sold. At what rate is the marginal revenue   changing when the number of units being sold is 35? Round your answer to four decimal places. ​

Accepted Answer

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

Question 9

Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. In this problem, use the graph of the function   given in the figure.   At what point(s) A through E is the rate of change of f (x) equal to zero?

Accepted Answer

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

Question 10

Find the second derivative. ​   ​

Accepted Answer

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

Question 11

Find the derivative of the given function, and use this to find x-values where the function has horizontal tangent lines. ​   ​

Accepted Answer

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

Question 12

Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other. In this problem, use the graph of the function   given in the figure.   Over what interval(s) (a) through (d) is the rate of change of f (x) positive?

Accepted Answer

A)  b c d 
B)  c 
C)  a b c d 
D)  a b c 
E)  a b d 
A)  b c d 
B)  c 
C)  a b c d 
D)  a b c 
E)  a b d

Question 13

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

Accepted Answer

A)  -6 
B)  -9 
C)  -1 
D)  3 
E)  does not exist 
A)  -6 
B)  -9 
C)  -1 
D)  3 
E)  does not exist

Question 14

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 15

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)  10 
B)  3 
C)    
D)  0 
E)  does not exist 
A)  10 
B)  3 
C)    
D)  0 
E)  does not exist

Question 16

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function   .
Is C continuous at   ?

Accepted Answer

A) True 
 B)False

Question 17

The cost per unit of producing a product is   dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $120, how many units should the firm produce and sell each week to maximize its profit? ​

Accepted Answer

A)  16 
B)  8 
C)  64 
D)  none 
E)  as many as possible 
A)  16 
B)  8 
C)  64 
D)  none 
E)  as many as possible

Question 18

Find the indicated derivative. ​   ​

Accepted Answer

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

Question 19

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. Is this function continuous for all

Accepted Answer

A) True 
 B)False

Question 20

Identify x-values where   has a maximum point or a minimum point, where   is increasing, and where   is decreasing. ​   ​

Accepted Answer

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

Determine whether the function is continuous or discontinuous at the given x-value.

Find and simplify.

Use properties of limits and algebraic methods to find the limit, if it exists.

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

Write the equation of the tangent line to each curve at the indicated point. As a check, graph both the function and the tangent line.

A graph of is shown and a c-value is given. For this problem, use the graph to find .

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.

The revenue (in thousands of dollars) from the sale of a product is , where x is the number of units sold. At what rate is the marginal revenue changing when the number of units being sold is 35? Round your answer to four decimal places.

Find the second derivative.

Find the derivative of the given function, and use this to find x-values where the function has horizontal tangent lines.

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

Find the derivative of the function.

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.

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function . Is C continuous at ?

The cost per unit of producing a product is dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $120, how many units should the firm produce and sell each week to maximize its profit?

Find the indicated derivative.

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. Is this function continuous for all

Identify x-values where has a maximum point or a minimum point, where is increasing, and where is decreasing.

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

Determine whether the function is continuous or discontinuous at the given x-value. ​ ​

Find and simplify. ​

Use properties of limits and algebraic methods to find the limit, if it exists. ​ ​

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

Write the equation of the tangent line to each curve at the indicated point. As a check, graph both the function and the tangent line. ​ ​

A graph of is shown and a c-value is given. For this problem, use the graph to find . ​ ​

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. ​ ​

The revenue (in thousands of dollars) from the sale of a product is , where x is the number of units sold. At what rate is the marginal revenue changing when the number of units being sold is 35? Round your answer to four decimal places. ​

Find the second derivative. ​ ​

Find the derivative of the given function, and use this to find x-values where the function has horizontal tangent lines. ​ ​

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

Find the derivative of the function. ​ ​

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. ​ ​

The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function . Is C continuous at ?

The cost per unit of producing a product is dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $120, how many units should the firm produce and sell each week to maximize its profit? ​

Find the indicated derivative. ​ ​

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. Is this function continuous for all

Identify x-values where has a maximum point or a minimum point, where is increasing, and where is decreasing. ​ ​

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

Determine whether the function is continuous or discontinuous at the given x-value.

Find and simplify.

Use properties of limits and algebraic methods to find the limit, if it exists.

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

Write the equation of the tangent line to each curve at the indicated point. As a check, graph both the function and the tangent line.

A graph of is shown and a c-value is given. For this problem, use the graph to find .

Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.

The revenue (in thousands of dollars) from the sale of a product is , where x is the number of units sold. At what rate is the marginal revenue changing when the number of units being sold is 35? Round your answer to four decimal places.

Find the second derivative.

Find the derivative of the given function, and use this to find x-values where the function has horizontal tangent lines.

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

Find the derivative of the function.

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.

The cost per unit of producing a product is dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $120, how many units should the firm produce and sell each week to maximize its profit?

Find the indicated derivative.

Identify x-values where has a maximum point or a minimum point, where is increasing, and where is decreasing.