Question 1

Find an equation of the line tangent to   . (Round coefficients to 3 decimal places.)

Accepted Answer

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

Question 2

Compute f '(2) for the function   .

Accepted Answer

A)  58 
B)  43 
C)  38 
D)  -43 
A)  58 
B)  43 
C)  38 
D)  -43 B

Question 3

Determine the real value(s) of x for which the line tangent to   is horizontal.

Accepted Answer

A)    
B)    
C)    
D)  x = 0 
A)    
B)    
C)    
D)  x = 0 C

Question 4

Find the second derivative,   , of   .

Accepted Answer

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

Question 5

Differentiate the function.

Accepted Answer

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

Question 6

Find an equation of the line tangent to   at   if   ,   ,   , and   .

Accepted Answer

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

Question 7

Find the third derivative of   .

Accepted Answer

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

Question 8

Compute f '(5) for the function   .

Accepted Answer

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

Question 9

Using the Mean Value Theorem, find a value of c that makes the conclusion true for

Accepted Answer

A)    
B)  One or more hypotheses fail 
C)    
D)      
A)    
B)  One or more hypotheses fail 
C)    
D)

Question 10

For   , find   .

Accepted Answer

A)  cos x 
B)  -cos x 
C)  sin x 
D)  -sin x 
A)  cos x 
B)  -cos x 
C)  sin x 
D)  -sin x

Question 11

Find the equation of the tangent line to the graph of y = f (x) at x = -2.

Accepted Answer

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

Question 12

Given that   , find   .

Accepted Answer

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

Question 13

Using the position function   , find the acceleration function.

Accepted Answer

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

Question 14

Use the position function   meters to find the velocity at time   seconds.

Accepted Answer

A)  3.1 m/sec 
B)  -9.8 m/sec 
C)  -1.8 m/sec 
D)  -4.9 m/sec 
A)  3.1 m/sec 
B)  -9.8 m/sec 
C)  -1.8 m/sec 
D)  -4.9 m/sec

Question 15

Given that   , find   .

Accepted Answer

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

Question 16

Given that   , find   .

Accepted Answer

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

Question 17

Find the derivative of the function.

Accepted Answer

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

Question 18

Find the derivative of the function.

Accepted Answer

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

Question 19

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. ...

Question 20

Using the Mean Value Theorem, find a value of c that makes the conclusion true for

Accepted Answer

A)  One or more hypotheses fail 
B)    
C)    
D)    
A)  One or more hypotheses fail 
B)    
C)    
D)

Find an equation of the line tangent to . (Round coefficients to 3 decimal places.)

Compute f '(2) for the function .

Determine the real value(s) of x for which the line tangent to is horizontal.

Find the second derivative, , of .

Differentiate the function.

Find an equation of the line tangent to at if , , , and .

Find the third derivative of .

Compute f '(5) for the function .

Using the Mean Value Theorem, find a value of c that makes the conclusion true for

For , find .

Find the equation of the tangent line to the graph of y = f (x) at x = -2.

Given that , find .

Using the position function , find the acceleration function.

Use the position function meters to find the velocity at time seconds.

Given that , find .

Given that , find .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

Using the Mean Value Theorem, find a value of c that makes the conclusion true for

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 3: Differentiation

Find an equation of the line tangent to . (Round coefficients to 3 decimal places.)

Compute f '(2) for the function .

Determine the real value(s) of x for which the line tangent to is horizontal.

Find the second derivative, , of .

Differentiate the function.

Find an equation of the line tangent to at if , , , and .

Find the third derivative of .

Compute f '(5) for the function .

Using the Mean Value Theorem, find a value of c that makes the conclusion true for

For , find .

Find the equation of the tangent line to the graph of y = f (x) at x = -2.

Given that , find .

Using the position function , find the acceleration function.

Use the position function meters to find the velocity at time seconds.

Given that , find .

Given that , find .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function.

Using the Mean Value Theorem, find a value of c that makes the conclusion true for

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters