Question 1

Differentiate the given function. ​   ​

Accepted Answer

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

Question 2

The graphs of a company's total revenue function   and total cost function   are shown. From the sale of 100 items, 500 items, and 700 items, rank from smallest to largest the amount of profit received. ​   ​

Accepted Answer

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

Question 3

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 at

Accepted Answer

A) True 
 B)False

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

Find the indicated derivative and simplify. ​   for   ​

Accepted Answer

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

Question 6

If   , find   . ​

Accepted Answer

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

Question 7

Find the third derivative. ​   ​

Accepted Answer

A)    
B)    
C)  0 
D)    
E)    
A)    
B)    
C)  0 
D)    
E)

Question 8

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

Accepted Answer

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

Question 9

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 10

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 11

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by   , and that the total cost function is given by   . Find the marginal profit function. ​

Accepted Answer

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

Question 12

If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is   . What is the acceleration of the object when   ? ​

Accepted Answer

A)  0 ft/sec2 
B)  -34 ft/sec2 
C)  86 ft/sec2 
D)  34 ft/sec2 
E)  -86 ft/sec2 
A)  0 ft/sec2 
B)  -34 ft/sec2 
C)  86 ft/sec2 
D)  34 ft/sec2 
E)  -86 ft/sec2

Question 13

For the function in this problem, approximate   by computing   with   . ​   ​

Accepted Answer

A)  -0.0171 
B)  0.2730 
C)  -1.0325 
D)  -0.0483 
E)  0.0537 
A)  -0.0171 
B)  0.2730 
C)  -1.0325 
D)  -0.0483 
E)  0.0537

Question 14

Use a table utility with x-values larger than 10,000 to investigate   . What does the table indicate about   ? ​   ​

Accepted Answer

A)  -3 
B)  3 
C)  6 
D)  0 
E)  does not exist 
A)  -3 
B)  3 
C)  6 
D)  0 
E)  does not exist

Question 15

The tangent line to the graph of f (x) at   is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line. ​   ​

Accepted Answer

A)  2 
B)  1 
C)  -4 
D)  5 
E)  does not exist 
A)  2 
B)  1 
C)  -4 
D)  5 
E)  does not exist

Question 16

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. ​   ​

Accepted Answer

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

Question 17

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is   Find the marginal revenue at   and tell what it predicts about the sale of the next unit. Round your answer to two decimal places. ​

Accepted Answer

A)  13.80. The selling of the next unit increases revenue by $13.80. 
B)  12.60. The selling of the next unit increases revenue by $12.60. 
C)  -414.00. The selling of the next unit decreases revenue by $414. 
D)  -30.00. The selling of the next unit decreases revenue by $30. 
E)  -15.00. The selling of the next unit decreases revenue by $15. 
A)  13.80. The selling of the next unit increases revenue by $13.80. 
B)  12.60. The selling of the next unit increases revenue by $12.60. 
C)  -414.00. The selling of the next unit decreases revenue by $414. 
D)  -30.00. The selling of the next unit decreases revenue by $30. 
E)  -15.00. The selling of the next unit decreases revenue by $15.

Question 18

Calculate the derivative of the function with the appropriate formula. ​   ​

Accepted Answer

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

Question 19

Suppose the graph shows a manufacturer's total revenue, in thousands of dollars, from the sale of x cellular telephones to dealers. Is the marginal revenue greater at 100 cell phones or at 500? ​   ​

Accepted Answer

A)  100 
B)  500 
A)  100 
B)  500

Question 20

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

Accepted Answer

A)    
B)    
C)  24 
D)  0 
E)    
A)    
B)    
C)  24 
D)  0 
E)

Differentiate the given function.

The graphs of a company's total revenue function and total cost function are shown. From the sale of 100 items, 500 items, and 700 items, rank from smallest to largest the amount of profit received.

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 at

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

Find the indicated derivative and simplify. for

If , find .

Find the third derivative.

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

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

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

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by , and that the total cost function is given by . Find the marginal profit function.

If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is . What is the acceleration of the object when ?

For the function in this problem, approximate by computing with .

Use a table utility with x-values larger than 10,000 to investigate . What does the table indicate about ?

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line.

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available.

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find the marginal revenue at and tell what it predicts about the sale of the next unit. Round your answer to two decimal places.

Calculate the derivative of the function with the appropriate formula.

Suppose the graph shows a manufacturer's total revenue, in thousands of dollars, from the sale of x cellular telephones to dealers. Is the marginal revenue greater at 100 cell phones or at 500?

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

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

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Exam 9: Derivatives

Differentiate the given function. ​ ​

The graphs of a company's total revenue function and total cost function are shown. From the sale of 100 items, 500 items, and 700 items, rank from smallest to largest the amount of profit received. ​ ​

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 at

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

Find the indicated derivative and simplify. ​ for ​

If , find . ​

Find the third derivative. ​ ​

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

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

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

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by , and that the total cost function is given by . Find the marginal profit function. ​

If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is . What is the acceleration of the object when ? ​

For the function in this problem, approximate by computing with . ​ ​

Use a table utility with x-values larger than 10,000 to investigate . What does the table indicate about ? ​ ​

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line. ​ ​

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. ​ ​

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find the marginal revenue at and tell what it predicts about the sale of the next unit. Round your answer to two decimal places. ​

Calculate the derivative of the function with the appropriate formula. ​ ​

Suppose the graph shows a manufacturer's total revenue, in thousands of dollars, from the sale of x cellular telephones to dealers. Is the marginal revenue greater at 100 cell phones or at 500? ​ ​

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

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

Differentiate the given function.

The graphs of a company's total revenue function and total cost function are shown. From the sale of 100 items, 500 items, and 700 items, rank from smallest to largest the amount of profit received.

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

Find the indicated derivative and simplify. for

If , find .

Find the third derivative.

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

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

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

In this problem, cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function is given by , and that the total cost function is given by . Find the marginal profit function.

If the formula describing the distance s (in feet) an object travels as a function of time t (in seconds) is . What is the acceleration of the object when ?

For the function in this problem, approximate by computing with .

Use a table utility with x-values larger than 10,000 to investigate . What does the table indicate about ?

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line.

Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available.

Total revenue is in dollars and x is the number of units. Suppose that the total revenue function for a commodity is Find the marginal revenue at and tell what it predicts about the sale of the next unit. Round your answer to two decimal places.

Calculate the derivative of the function with the appropriate formula.

Suppose the graph shows a manufacturer's total revenue, in thousands of dollars, from the sale of x cellular telephones to dealers. Is the marginal revenue greater at 100 cell phones or at 500?

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