Question 1

Suppose the total revenue function for a blender is   where x is the number of units sold. What function gives the marginal revenue? ​

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. Find the instantaneous rate of change of the average cost   for any level of production. ​

Accepted Answer

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

Question 3

For the function in this problem, find the instantaneous rate of change of the function at the given value. ​   ;   ​

Accepted Answer

A)  18 
B)  6 
C)  10 
D)  14 
E)  13 
A)  18 
B)  6 
C)  10 
D)  14 
E)  13

Question 4

If the profit function for a product is given by   , find   . ​

Accepted Answer

A)  -3,600 
B)  -1,600 
C)  -2,725 
D)  -4,100 
E)  does not exist 
A)  -3,600 
B)  -1,600 
C)  -2,725 
D)  -4,100 
E)  does not exist

Question 5

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, 401st item, and 701st item, rank from smallest to largest the amount of profit received. ​   ​

Accepted Answer

A)  701st, 51st, 401st 
B)  401st, 701st, 51st 
C)  701st, 401st, 51st 
D)  51st, 701st, 401st 
E)  51st, 401st, 701st 
A)  701st, 51st, 401st 
B)  401st, 701st, 51st 
C)  701st, 401st, 51st 
D)  51st, 701st, 401st 
E)  51st, 401st, 701st

Question 6

For the function in this problem, find the derivative, by using the definition. ​   ​

Accepted Answer

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

Question 7

Find the indicated derivative. ​   .
​

Accepted Answer

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

Question 8

The graph of a company's profit function is shown. For the given problem, use the graph to answer the following question about points A, B, and C. Rank from smallest to largest the amounts of profit received at these points. ​   ​

Accepted Answer

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

Question 9

Differentiate the given function. ​   ​

Accepted Answer

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

Question 10

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

Accepted Answer

A)  5 
B)  -15 
C)  0 
D)  15 
E)  does not exist 
A)  5 
B)  -15 
C)  0 
D)  15 
E)  does not exist

Question 11

Given   , find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: ​   and   ​

Accepted Answer

A)  17.9 and 17.99 
B)  20.9 and 20.99 
C)  19.90 and 19.99 
D)  19.90 and 20.99 
E)  17.9 and 19.99 
A)  17.9 and 17.99 
B)  20.9 and 20.99 
C)  19.90 and 19.99 
D)  19.90 and 20.99 
E)  17.9 and 19.99

Question 12

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

Accepted Answer

A)  -6 
B)  0 
C)  8 
D)  2 
E)  does not exist 
A)  -6 
B)  0 
C)  8 
D)  2 
E)  does not exist

Question 13

Suppose the figure shows the total cost graph for a company. Arrange the average rates of change of total cost from A to B, B to C, and A to C from smallest to greatest. ​   ​

Accepted Answer

A)  A to B then A to C then B to C 
B)  B to C then A to C then A to B 
C)  A to C then A to B then B to C 
D)  A to C then B to C then A to B 
E)  A to B then B to C then A to C 
A)  A to B then A to C then B to C 
B)  B to C then A to C then A to B 
C)  A to C then A to B then B to C 
D)  A to C then B to C then A to B 
E)  A to B then B to C then A to C

Question 14

For the given function, find the slope of the tangent line at   . ​   ​

Accepted Answer

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

Question 15

If the revenue for a product (in dollars) is   , and the average revenue per unit is   ,   , find   . ​

Accepted Answer

A)  $900 per unit 
B)  $0.7 per unit 
C)  $90 per unit 
D)  $0 per unit 
E)  does not exist 
A)  $900 per unit 
B)  $0.7 per unit 
C)  $90 per unit 
D)  $0 per unit 
E)  does not exist

Question 16

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 17

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   . Round your answer to two decimal places. ​

Accepted Answer

A)  $5,700.00 
B)  $4,350.00 
C)  $1,350.00 
D)  $55.00 
E)  $2.00 
A)  $5,700.00 
B)  $4,350.00 
C)  $1,350.00 
D)  $55.00 
E)  $2.00

Question 18

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 19

Differentiate the given function. ​   ​

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)  -5,774. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $5,774. 
B)  -241. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $241. 
C)  -241. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $241. 
D)  -120. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $120. 
E)  -120. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $120. 
A)  -5,774. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $5,774. 
B)  -241. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $241. 
C)  -241. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $241. 
D)  -120. If the price of an oil change goes from $40 to $41, the monthly sales volume will decrease by $120. 
E)  -120. If the price of an oil change goes from $40 to $41, the monthly sales volume will increase by $120.

Suppose the total revenue function for a blender is where x is the number of units sold. What function gives the marginal revenue?

Suppose that the total cost function, in dollars, for a certain commodity is given by , where x is the number of units produced. Find the instantaneous rate of change of the average cost for any level of production.

For the function in this problem, find the instantaneous rate of change of the function at the given value. ;

If the profit function for a product is given by , find .

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, 401st item, and 701st item, rank from smallest to largest the amount of profit received.

For the function in this problem, find the derivative, by using the definition.

Find the indicated derivative. .

The graph of a company's profit function is shown. For the given problem, use the graph to answer the following question about points A, B, and C. Rank from smallest to largest the amounts of profit received at these points.

Differentiate the given function.

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

Given , find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: and

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

Suppose the figure shows the total cost graph for a company. Arrange the average rates of change of total cost from A to B, B to C, and A to C from smallest to greatest.

For the given function, find the slope of the tangent line at .

If the revenue for a product (in dollars) is , and the average revenue per unit is , , find .

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

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 . Round your answer to two decimal places.

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.

Differentiate the given function.

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.

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

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Exam 9: Derivatives

Suppose the total revenue function for a blender is where x is the number of units sold. What function gives the marginal revenue? ​

Suppose that the total cost function, in dollars, for a certain commodity is given by , where x is the number of units produced. Find the instantaneous rate of change of the average cost for any level of production. ​

For the function in this problem, find the instantaneous rate of change of the function at the given value. ​ ; ​

If the profit function for a product is given by , find . ​

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, 401st item, and 701st item, rank from smallest to largest the amount of profit received. ​ ​

For the function in this problem, find the derivative, by using the definition. ​ ​

Find the indicated derivative. ​ . ​

The graph of a company's profit function is shown. For the given problem, use the graph to answer the following question about points A, B, and C. Rank from smallest to largest the amounts of profit received at these points. ​ ​

Differentiate the given function. ​ ​

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

Given , find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: ​ and ​

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

Suppose the figure shows the total cost graph for a company. Arrange the average rates of change of total cost from A to B, B to C, and A to C from smallest to greatest. ​ ​

For the given function, find the slope of the tangent line at . ​ ​

If the revenue for a product (in dollars) is , and the average revenue per unit is , , find . ​

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

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 . Round your answer to two decimal places. ​

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. ​ ​

Differentiate the given function. ​ ​

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. ​

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 the total revenue function for a blender is where x is the number of units sold. What function gives the marginal revenue?

Suppose that the total cost function, in dollars, for a certain commodity is given by , where x is the number of units produced. Find the instantaneous rate of change of the average cost for any level of production.

For the function in this problem, find the instantaneous rate of change of the function at the given value. ;

If the profit function for a product is given by , find .

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, 401st item, and 701st item, rank from smallest to largest the amount of profit received.

For the function in this problem, find the derivative, by using the definition.

Find the indicated derivative. .

The graph of a company's profit function is shown. For the given problem, use the graph to answer the following question about points A, B, and C. Rank from smallest to largest the amounts of profit received at these points.

Differentiate the given function.

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

Given , find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: and

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

Suppose the figure shows the total cost graph for a company. Arrange the average rates of change of total cost from A to B, B to C, and A to C from smallest to greatest.

For the given function, find the slope of the tangent line at .

If the revenue for a product (in dollars) is , and the average revenue per unit is , , find .

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

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 . Round your answer to two decimal places.

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.

Differentiate the given function.

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.