Question 1

Find the derivative of   .

Accepted Answer

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

Question 2

Find the derivative of   .

Accepted Answer

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

Question 3

Using the position function   , find the acceleration function.

Accepted Answer

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

Question 4

Find a formula for the nth derivative   of

Accepted Answer

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

Question 5

Find all the functions

Accepted Answer

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

Question 6

Differentiate the function.

Accepted Answer

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

Question 7

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

Accepted Answer

A)  x = -2, x = 2 
B)  x = 0, x = -2, x = 2 
C)  x = 0 
D)  x = 0, x = 2 
A)  x = -2, x = 2 
B)  x = 0, x = -2, x = 2 
C)  x = 0 
D)  x = 0, x = 2

Question 8

Estimate the slope of the tangent line to the curve at x = 2.

Accepted Answer

A)  2 
B)  -2 
C)    
D)    
A)  2 
B)  -2 
C)    
D)

Question 9

Find the derivative of   .

Accepted Answer

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

Question 10

Use the position function   meters to find the velocity at t = 4 seconds.

Accepted Answer

A)  9 m/s 
B)    m/s 
C)    m/s 
D)    m/s 
A)  9 m/s 
B)    m/s 
C)    m/s 
D)    m/s

Question 11

Using the position function   , find the velocity function.

Accepted Answer

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

Question 12

Find an equation of the tangent line to y = f(x) at x = 4.

Accepted Answer

A)  y = 21x - 64 
B)  y = -96x - 251 
C)  y = 96x - 251 
D)  y = 96x + 251 
A)  y = 21x - 64 
B)  y = -96x - 251 
C)  y = 96x - 251 
D)  y = 96x + 251

Question 13

Use the position function to find the velocity at time   Assume units of feet and seconds.

Accepted Answer

A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec 
A)    ft/sec 
B)    ft/sec 
C)    ft/sec 
D)    ft/sec

Question 14

Find the equation of the tangent line to   at

Accepted Answer

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

Question 15

Find the derivative of   .

Accepted Answer

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

Question 16

Find the derivative of   .

Accepted Answer

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

Question 17

Below is a graph of   . Sketch a plausible graph of a continuous function   .

Accepted Answer

Answers ma

Question 18

Find the derivative   implicitly if   .

Accepted Answer

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

Question 19

Find an equation of the tangent line at the given point.   at

Accepted Answer

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

Question 20

Find the derivative where f is an unspecified differentiable function.

Accepted Answer

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

Find the derivative of .

Find the derivative of .

Using the position function , find the acceleration function.

Find a formula for the nth derivative of

Find all the functions

Differentiate the function.

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

Estimate the slope of the tangent line to the curve at x = 2.

Find the derivative of .

Use the position function meters to find the velocity at t = 4 seconds.

Using the position function , find the velocity function.

Find an equation of the tangent line to y = f(x) at x = 4.

Use the position function to find the velocity at time Assume units of feet and seconds.

Find the equation of the tangent line to at

Find the derivative of .

Find the derivative of .

Below is a graph of . Sketch a plausible graph of a continuous function .

Find the derivative implicitly if .

Find an equation of the tangent line at the given point. at

Find the derivative where f is an unspecified differentiable function.

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 the derivative of .

Find the derivative of .

Using the position function , find the acceleration function.

Find a formula for the nth derivative of

Find all the functions

Differentiate the function.

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

Estimate the slope of the tangent line to the curve at x = 2.

Find the derivative of .

Use the position function meters to find the velocity at t = 4 seconds.

Using the position function , find the velocity function.

Find an equation of the tangent line to y = f(x) at x = 4.

Use the position function to find the velocity at time Assume units of feet and seconds.

Find the equation of the tangent line to at

Find the derivative of .

Find the derivative of .

Below is a graph of . Sketch a plausible graph of a continuous function .

Find the derivative implicitly if .

Find an equation of the tangent line at the given point. at

Find the derivative where f is an unspecified differentiable function.

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