Question 1

Find an equation of the tangent line to the graph of the function   at the point   .

Accepted Answer

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

Question 2

Suppose that an automobile's velocity starting from rest is   where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.

Accepted Answer

A) 7.4 ft/sec2 
B) 0.4 ft/sec2 
C) 1.7 ft/sec2 
D) 0.8 ft/sec2 
E) 0.2 ft/sec2 
A) 7.4 ft/sec2 
B) 0.4 ft/sec2 
C) 1.7 ft/sec2 
D) 0.8 ft/sec2 
E) 0.2 ft/sec2 D

Question 3

Find the second derivative of the function   .

Accepted Answer

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

Question 4

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

Accepted Answer

A) -128.406 ft/sec 
B) -256.811 ft/sec 
C) -111.203 ft/sec 
D) -267.298 ft/sec 
E) -244.811 ft/sec 
A) -128.406 ft/sec 
B) -256.811 ft/sec 
C) -111.203 ft/sec 
D) -267.298 ft/sec 
E) -244.811 ft/sec

Question 5

A conical tank (with vertex down) is 20 feet across the top and 26 feet deep. If water is flowing into the tank at a rate of 16 cubic feet per minute, find the rate of change of the depth of the water when the water is 12 feet deep.

Accepted Answer

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

Question 6

The graph of the function f is given below. Select the graph of

Accepted Answer

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

Question 7

Use the alternative form of the derivative to find the derivative of the function   at   .

Accepted Answer

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

Question 8

Suppose the position function for a free-falling object on a certain planet is given by is given by   . A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.

Accepted Answer

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

Question 9

Suppose the position function for a free-falling object on a certain planet is given by   . A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when   .

Accepted Answer

A) -15 ft/sec 
B) -45 ft/sec 
C) -29 ft/sec 
D) -30 ft/sec 
E) -44 ft/sec 
A) -15 ft/sec 
B) -45 ft/sec 
C) -29 ft/sec 
D) -30 ft/sec 
E) -44 ft/sec

Question 10

Use the Quotient Rule to differentiate the function   .

Accepted Answer

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

Question 11

Find the derivative of the function.

Accepted Answer

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

Question 12

Find an equation of the tangent line to the graph of the function   at the point   .

Accepted Answer

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

Question 13

Differentiate   with respect to t (x and y are functions of t).

Accepted Answer

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

Question 14

Use the rules of differentiation to find the derivative of the function   .

Accepted Answer

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

Question 15

Find the slope m of the line tangent to the graph of the function   at the point   .

Accepted Answer

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

Question 16

Find the second derivative of the function.

Accepted Answer

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

Question 17

A projectile is shot upwards from the surface of the earth with an initial velocity of 148 meters per second. The position function is   .What is its velocity after 4 seconds?

Accepted Answer

A) The velocity after 4 seconds is 128.4 meters per second. 
B) The velocity after 4 seconds is -167.6 meters per second. 
C) The velocity after 4 seconds is -187.2 meters per second. 
D) The velocity after 4 seconds is 108.8 meters per second. 
E) The velocity after 4 seconds is 276.4 meters per second. 
A) The velocity after 4 seconds is 128.4 meters per second. 
B) The velocity after 4 seconds is -167.6 meters per second. 
C) The velocity after 4 seconds is -187.2 meters per second. 
D) The velocity after 4 seconds is 108.8 meters per second. 
E) The velocity after 4 seconds is 276.4 meters per second.

Question 18

Find the derivative of the following function using the limiting process.

Accepted Answer

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

Question 19

Find the derivative of the algebraic function   .

Accepted Answer

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

Question 20

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when r = 9 inches.

Accepted Answer

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

Find an equation of the tangent line to the graph of the function at the point .

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.

Find the second derivative of the function .

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

A conical tank (with vertex down) is 20 feet across the top and 26 feet deep. If water is flowing into the tank at a rate of 16 cubic feet per minute, find the rate of change of the depth of the water when the water is 12 feet deep.

The graph of the function f is given below. Select the graph of

Use the alternative form of the derivative to find the derivative of the function at .

Suppose the position function for a free-falling object on a certain planet is given by is given by . A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when .

Use the Quotient Rule to differentiate the function .

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function at the point .

Differentiate with respect to t (x and y are functions of t).

Use the rules of differentiation to find the derivative of the function .

Find the slope m of the line tangent to the graph of the function at the point .

Find the second derivative of the function.

A projectile is shot upwards from the surface of the earth with an initial velocity of 148 meters per second. The position function is .What is its velocity after 4 seconds?

Find the derivative of the following function using the limiting process.

Find the derivative of the algebraic function .

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when r = 9 inches.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 5: Differentiation

Find an equation of the tangent line to the graph of the function at the point .

Suppose that an automobile's velocity starting from rest is where v is measured in feet per second. Find the acceleration at 9 seconds. Round your answer to one decimal place.

Find the second derivative of the function .

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1374 feet tall. Find velocity of the coin at impact. Round your answer to the three decimal places.

A conical tank (with vertex down) is 20 feet across the top and 26 feet deep. If water is flowing into the tank at a rate of 16 cubic feet per minute, find the rate of change of the depth of the water when the water is 12 feet deep.

The graph of the function f is given below. Select the graph of

Use the alternative form of the derivative to find the derivative of the function at .

Suppose the position function for a free-falling object on a certain planet is given by is given by . A silver coin is dropped from the top of a building that is 1366 feet tall. Determine the velocity function for the coin.

Suppose the position function for a free-falling object on a certain planet is given by . A silver coin is dropped from the top of a building that is 1362 feet tall. Find the instantaneous velocity of the coin when .

Use the Quotient Rule to differentiate the function .

Find the derivative of the function.

Find an equation of the tangent line to the graph of the function at the point .

Differentiate with respect to t (x and y are functions of t).

Use the rules of differentiation to find the derivative of the function .

Find the slope m of the line tangent to the graph of the function at the point .

Find the second derivative of the function.

A projectile is shot upwards from the surface of the earth with an initial velocity of 148 meters per second. The position function is .What is its velocity after 4 seconds?

Find the derivative of the following function using the limiting process.

Find the derivative of the algebraic function .

The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when r = 9 inches.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters