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)

Question 2

The monthly output of a certain product is   where x is the capital investment in millions of dollars. Find   which can be used to estimate the effect on the output if an additional capital investment of $1 million is made. ​

Accepted Answer

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

Question 3

A certain calling card costs 6.1 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 61 cent connection fee. If   is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. ​   ​

Accepted Answer

A) $0 
B) $0.61 
C) $0.73 
D) $0.67 
E) does not exist 
A) $0 
B) $0.61 
C) $0.73 
D) $0.67 
E) does not exist

Question 4

McRobert's TV Shop sells 400 sets per month, at a price of $600 per unit. Market research indicates that the shop can sell one additional set for each $1 it reduces the price. The total revenue (in dollars) is given by   , where x is the number of additional sets beyond the original 400. What is the marginal revenue if 300 more units are sold? ​

Accepted Answer

A) 0$1,600 
B) ​-$100 
C) 0$400 
D) -$400 
E) 0$800 
A) 0$1,600 
B) ​-$100 
C) 0$400 
D) -$400 
E) 0$800

Question 5

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 6

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 7

For the given function, find the average rate of change over the specified interval. ​   over   ​

Accepted Answer

A) 0 
B) -2 
C) 6 
D) -34 
E) 34 
A) 0 
B) -2 
C) 6 
D) -34 
E) 34

Question 8

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 9

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

Accepted Answer

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

Question 10

Find the indicated derivative. Find   ​

Accepted Answer

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

Question 11

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. Find   . ​   ​

Accepted Answer

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

Question 12

Find the indicated derivative. ​   .
​

Accepted Answer

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

Question 13

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to   where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places. ​

Accepted Answer

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

Question 14

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 15

Given the graph of   in the figure, determine all x-values from F, G, H, or I for which the function is continuous. ​   ​

Accepted Answer

A) G H 
B) G H I 
C) F G H I 
D) F G 
E) G 
A) G H 
B) G H I 
C) F G H I 
D) F G 
E) G

Question 16

Find the slope of the tangent at   ​   ​

Accepted Answer

A) 19 
B) 17 
C) 29 
D) 7 
E) 32 
A) 19 
B) 17 
C) 29 
D) 7 
E) 32

Question 17

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

Accepted Answer

A)    
B)   
Or   
C)    
D)    
E)   
And   
A)    
B)   
Or   
C)    
D)    
E)   
And

Question 18

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

Accepted Answer

A) 192 
B) -24 
C) 480 
D) 168 
E) does not exist 
A) 192 
B) -24 
C) 480 
D) 168 
E) does not exist

Question 19

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)   
In/sec 
B)   
In/sec 
C)   
In/sec 
D)   
In/sec 
E)   
In/sec 
A)   
In/sec 
B)   
In/sec 
C)   
In/sec 
D)   
In/sec 
E)   
In/sec

Question 20

Suppose that the revenue (in dollars) from the sale of a product is given by   , where x is the number of units sold. How fast is the marginal revenue   changing when   ​

Accepted Answer

A) 1.4 dollars per unit 
B) -30 dollars per unit 
C) 30 dollars per unit 
D) -0.1 dollars per unit 
E) -1.4 dollars per unit 
A) 1.4 dollars per unit 
B) -30 dollars per unit 
C) 30 dollars per unit 
D) -0.1 dollars per unit 
E) -1.4 dollars per unit

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

The monthly output of a certain product is where x is the capital investment in millions of dollars. Find which can be used to estimate the effect on the output if an additional capital investment of $1 million is made.

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.

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

For the given function, find the average rate of change over the specified interval. over

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

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

Find the indicated derivative. Find

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. Find .

Find the indicated derivative. .

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places.

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

Given the graph of in the figure, determine all x-values from F, G, H, or I for which the function is continuous.

Find the slope of the tangent at

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

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

Suppose that the revenue (in dollars) from the sale of a product is given by , where x is the number of units sold. How fast is the marginal revenue changing when

Algebraic Concepts

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; Data Description

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 10: Derivatives

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

The monthly output of a certain product is where x is the capital investment in millions of dollars. Find which can be used to estimate the effect on the output if an additional capital investment of $1 million is made. ​

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. ​ ​

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

For the given function, find the average rate of change over the specified interval. ​ over ​

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

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

Find the indicated derivative. Find ​

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. Find . ​ ​

Find the indicated derivative. ​ . ​

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places. ​

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

Given the graph of in the figure, determine all x-values from F, G, H, or I for which the function is continuous. ​ ​

Find the slope of the tangent at ​ ​

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

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

Suppose that the revenue (in dollars) from the sale of a product is given by , where x is the number of units sold. How fast is the marginal revenue changing when ​

Algebraic Concepts

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; Data Description

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

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

The monthly output of a certain product is where x is the capital investment in millions of dollars. Find which can be used to estimate the effect on the output if an additional capital investment of $1 million is made.

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.

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

For the given function, find the average rate of change over the specified interval. over

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

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

Find the indicated derivative. Find

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. Find .

Find the indicated derivative. .

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places.

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

Given the graph of in the figure, determine all x-values from F, G, H, or I for which the function is continuous.

Find the slope of the tangent at

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

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

Suppose that the revenue (in dollars) from the sale of a product is given by , where x is the number of units sold. How fast is the marginal revenue changing when