Question 1

Determine if the function   is increasing, decreasing, or neither.

Accepted Answer

A)  Increasing 
B)  Decreasing 
C)  Neither 
A)  Increasing 
B)  Decreasing 
C)  Neither

Question 2

Find the derivative of   .

Accepted Answer

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

Question 3

Find the derivative of   .

Accepted Answer

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

Question 4

Find the derivative of   .

Accepted Answer

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

Question 5

Compute the slope of the line tangent to   .

Accepted Answer

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

Question 6

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

Accepted Answer

A)    m/sec 
B)    m/sec 
C)    m/sec 
D)    m/sec 
A)    m/sec 
B)    m/sec 
C)    m/sec 
D)    m/sec

Question 7

Find the second derivative of the function.

Accepted Answer

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

Question 8

Find the second derivative of   .

Accepted Answer

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

Question 9

Compute the slopes of the secant lines between the point at x = 1 and points close to it (such as x = 0, x = 2, x = 0.9, x = 1.1) and use these results to estimate the slope of the tangent line at x = 1. Round to two decimal places.

Accepted Answer

A)  -1.30 
B)  -0.70 
C)  -0.20 
D)  0.50 
A)  -1.30 
B)  -0.70 
C)  -0.20 
D)  0.50

Question 10

Use the graph of   below to sketch the graph of   on the same axes. (Hint: sketch   first.)

Accepted Answer

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

Question 11

Find all the functions

Accepted Answer

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

Question 12

Sketch the graph of a function with the following properties:           and

Accepted Answer

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

Question 13

Below is a graph of   . Sketch a graph of   .

Accepted Answer

The answer of Below is a graph of  ...

Question 14

Find the derivative of   .

Accepted Answer

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

Question 15

Compute the derivative of   at x = -8 where   .

Accepted Answer

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

Question 16

Find the average velocity for an object between t = -1 sec and t = -0.9 sec if f(t) = 5sin(t) + 5 represents its position in feet. (Round to the nearest thousandth.)

Accepted Answer

A)  2.702 
B)  3.108 
C)  2.907 
D)  -2.907 
A)  2.702 
B)  3.108 
C)  2.907 
D)  -2.907

Determine if the function is increasing, decreasing, or neither.

Find the derivative of .

Find the derivative of .

Find the derivative of .

Compute the slope of the line tangent to .

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

Find the second derivative of the function.

Find the second derivative of .

Compute the slopes of the secant lines between the point at x = 1 and points close to it (such as x = 0, x = 2, x = 0.9, x = 1.1) and use these results to estimate the slope of the tangent line at x = 1. Round to two decimal places.

Use the graph of below to sketch the graph of on the same axes. (Hint: sketch first.)

Find all the functions

Sketch the graph of a function with the following properties: and

Below is a graph of . Sketch a graph of .

Find the derivative of .

Compute the derivative of at x = -8 where .

Find the average velocity for an object between t = -1 sec and t = -0.9 sec if f(t) = 5sin(t) + 5 represents its position in feet. (Round to the nearest thousandth.)

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

Determine if the function is increasing, decreasing, or neither.

Find the derivative of .

Find the derivative of .

Find the derivative of .

Compute the slope of the line tangent to .

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

Find the second derivative of the function.

Find the second derivative of .

Compute the slopes of the secant lines between the point at x = 1 and points close to it (such as x = 0, x = 2, x = 0.9, x = 1.1) and use these results to estimate the slope of the tangent line at x = 1. Round to two decimal places.

Use the graph of below to sketch the graph of on the same axes. (Hint: sketch first.)

Find all the functions

Sketch the graph of a function with the following properties: and

Below is a graph of . Sketch a graph of .

Find the derivative of .

Compute the derivative of at x = -8 where .

Find the average velocity for an object between t = -1 sec and t = -0.9 sec if f(t) = 5sin(t) + 5 represents its position in feet. (Round to the nearest thousandth.)

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