Question 1

Find y '( $\pi$) where   .

Accepted Answer

$\pi$² + 1

Question 2

Given   , find the slope of the graph of f at the x-value x0 = 3.

Accepted Answer

108

Question 3

Find the instantaneous rate of change of   with respect to x at x0 = 5.

Accepted Answer

A)  -175 
B)  -6.9600 
C)  0.2800 
D)  -0.2800 
E)  -0.1020 
A)  -175 
B)  -6.9600 
C)  0.2800 
D)  -0.2800 
E)  -0.1020 D

Question 4

Find f '(u) if   .

Accepted Answer

The answer of Find f '(u) if   ....

Question 5

Find f '(x) if f(x) = cos(x6).

Accepted Answer

- 6x<sup>5

Question 6

Find an equation for the tangent line to the graph of y = x sin x at x =  $\pi$

Accepted Answer

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

Question 7

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 8

Find f '(x) if f(x) = (x2 + 5)(x3 - 4x2 + x).

Accepted Answer

f '(x) = 5

Question 9

Find the equations of the tangent and normal to the graph of   at x = 4.

Accepted Answer

Tangent li

Question 10

Find   if y = 8x sin x - 3 cos x + x2 cos x.

Accepted Answer

Question 11

Find f '(x) if f(x) = csc2x + cot2x.

Accepted Answer

A)  2 csc x + 2 cot x 
B)  2 csc x - 2 cot x 
C)  -1 
D)  1 
E)  0 
A)  2 csc x + 2 cot x 
B)  2 csc x - 2 cot x 
C)  -1 
D)  1 
E)  0

Question 12

Find the equation of the line tangent to the graph of y = sin x at the point where x = 0.

Accepted Answer

A)  y = cos x 
B)  y = x 
C)  y = -x 
A)  y = cos x 
B)  y = x 
C)  y = -x

Question 13

Answer true or false. Use a graphing utility to graph y = 4t3 on [0, 3]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is increasing over the graphed domain.

Accepted Answer

A) True 
 B)False

Question 14

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 15

Use a graphing utility to show that   does not have a derivative everywhere.

Accepted Answer

There is no tangent

Question 16

The volume of a sphere is given by   where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of V with respect to r when r = 6.

Accepted Answer

The instan

Question 17

Let   . Find the instantaneous rate of change of y with respect to x at the point x = 2.

Accepted Answer

The answer of Let   . Find the instantaneous...

Question 18

Use a graphing utility to obtain the graph of   . Determine the slope of the tangent line to the graph at x = 0.

Accepted Answer

A)    
B)  0 
C)  3 
D)  16 
E)  8 
A)    
B)  0 
C)  3 
D)  16 
E)  8

Question 19

Answer true or false. Using a graphing utility it can be shown that   is differentiable everywhere on [-10, 10].

Accepted Answer

A) True 
 B)False

Question 20

The graph shows the position versus time curve for a particle moving on a straight line. Is the instantaneous velocity increasing or decreasing with time?

Accepted Answer

The answer of The graph shows the position versus time...

Find y '( $\pi$ ) where $Find y '( \pi ) where .$ .

Given , find the slope of the graph of f at the x-value x₀ = 3.

Find the instantaneous rate of change of with respect to x at x₀ = 5.

Find f '(u) if .

Find f '(x) if f(x) = cos(x⁶).

Find an equation for the tangent line to the graph of y = x sin x at x = $\pi$

Find if .

Find f '(x) if f(x) = (x² + 5)(x³ - 4x² + x).

Find the equations of the tangent and normal to the graph of at x = 4.

Find if y = 8x sin x - 3 cos x + x² cos x.

Find f '(x) if f(x) = csc²x + cot²x.

Find the equation of the line tangent to the graph of y = sin x at the point where x = 0.

Answer true or false. Use a graphing utility to graph y = 4t³ on [0, 3]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is increasing over the graphed domain.

Find if .

Use a graphing utility to show that does not have a derivative everywhere.

The volume of a sphere is given by where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of V with respect to r when r = 6.

Let . Find the instantaneous rate of change of y with respect to x at the point x = 2.

Use a graphing utility to obtain the graph of . Determine the slope of the tangent line to the graph at x = 0.

Answer true or false. Using a graphing utility it can be shown that is differentiable everywhere on [-10, 10].

The graph shows the position versus time curve for a particle moving on a straight line. Is the instantaneous velocity increasing or decreasing with time?

Limits and Continuity

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 2: The Derivative

Find y '( π\piπ ) where .

Given , find the slope of the graph of f at the x-value x0 = 3.

Find the instantaneous rate of change of with respect to x at x0 = 5.

Find f '(u) if .

Find f '(x) if f(x) = cos(x6).

Find an equation for the tangent line to the graph of y = x sin x at x = π\piπ

Find if .

Find f '(x) if f(x) = (x2 + 5)(x3 - 4x2 + x).

Find the equations of the tangent and normal to the graph of at x = 4.

Find if y = 8x sin x - 3 cos x + x2 cos x.

Find f '(x) if f(x) = csc2x + cot2x.

Find the equation of the line tangent to the graph of y = sin x at the point where x = 0.

Answer true or false. Use a graphing utility to graph y = 4t3 on [0, 3]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is increasing over the graphed domain.

Find if .

Use a graphing utility to show that does not have a derivative everywhere.

The volume of a sphere is given by where r is the radius of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of V with respect to r when r = 6.

Let . Find the instantaneous rate of change of y with respect to x at the point x = 2.

Use a graphing utility to obtain the graph of . Determine the slope of the tangent line to the graph at x = 0.

Answer true or false. Using a graphing utility it can be shown that is differentiable everywhere on [-10, 10].

The graph shows the position versus time curve for a particle moving on a straight line. Is the instantaneous velocity increasing or decreasing with time?

Limits and Continuity

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find y '( $\pi$ ) where $Find y '( \pi ) where .$ .

Given , find the slope of the graph of f at the x-value x₀ = 3.

Find the instantaneous rate of change of with respect to x at x₀ = 5.

Find f '(x) if f(x) = cos(x⁶).

Find an equation for the tangent line to the graph of y = x sin x at x = $\pi$

Find f '(x) if f(x) = (x² + 5)(x³ - 4x² + x).

Find if y = 8x sin x - 3 cos x + x² cos x.

Find f '(x) if f(x) = csc²x + cot²x.

Answer true or false. Use a graphing utility to graph y = 4t³ on [0, 3]. If this graph represents a position versus time curve for a particle, the instantaneous velocity of the particle is increasing over the graphed domain.