Question 1

Find f '(s) if f(s) = (6s2 + 8)(s2 - 7s).

Accepted Answer

f '(s) = 12s (s² - 7s

Question 2

If   , find   .

Accepted Answer

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

Question 3

y = sin3( $\pi$ - 9$\theta$ ). Find dy/d$\theta$ .

Accepted Answer

A)  - 27 cos( $\pi$ - 9$\theta$ ) sin2( $\pi$ - 9$\theta$ ) 
B)  - 27 cos( $\pi$ + 9$\theta$ ) sin2( $\pi$ + 9$\theta$ ) 
C)  - 27 cos 2( $\pi$ - 9$\theta$ ) sin( $\pi$ - 9$\theta$ ) 
D)  - cos( $\pi$ - 9$\theta$ ) sin2( $\pi$ - 9$\theta$ ) 
E)  - 27 sin2( $\pi$ - 9$\theta$ ) 
A)  - 27 cos( $\pi$ - 9$\theta$ ) sin2( $\pi$ - 9$\theta$ ) 
B)  - 27 cos( $\pi$ + 9$\theta$ ) sin2( $\pi$ + 9$\theta$ ) 
C)  - 27 cos 2( $\pi$ - 9$\theta$ ) sin( $\pi$ - 9$\theta$ ) 
D)  - cos( $\pi$ - 9$\theta$ ) sin2( $\pi$ - 9$\theta$ ) 
E)  - 27 sin2( $\pi$ - 9$\theta$ )

Question 4

Given that f(2) = -2 and f '(2) = -2, find an equation for the tangent line to the graph of y = f(x) at the point where x = 2.

Accepted Answer

The answer of Given that f(2) = -2 and f...

Question 5

An object moves in a straight line so that after t s its distance in mm from its original position is given by s = 3t3 + 4t. Its instantaneous velocity at t = 3s is

Accepted Answer

A)  81 mm 
B)  247 mm 
C)  733 mm 
D)  85 mm 
E)  31 mm 
A)  81 mm 
B)  247 mm 
C)  733 mm 
D)  85 mm 
E)  31 mm

Question 6

Answer true or false. Use a graphing utility to help in obtaining the graph of y = f(x) = |x - 11|. The derivative f '(x) is not defined at x = 11.

Accepted Answer

A) True 
 B)False

Question 7

Find f '(x) if f(x) = (x5 - 11)10.

Accepted Answer

A)  10x4(x5 - 11)9 
B)  5x4(x5 - 11)9 
C)  50(x5 - 11)9 
D)  50x4(x5 - 11)9 
E)  10(x5 - 11)9 
A)  10x4(x5 - 11)9 
B)  5x4(x5 - 11)9 
C)  50(x5 - 11)9 
D)  50x4(x5 - 11)9 
E)  10(x5 - 11)9

Question 8

If   ,

Accepted Answer

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

Question 9

If f(6) = 48, f '(6) = 5, g(6) = 4, g '(6) = -3, find F'(6) if F(x) =   .

Accepted Answer

The answer of If f(6) = 48, f '(6) =...

Question 10

Find   where

Accepted Answer

The answer of Find   where  ...

Question 11

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 12

Find f'($\theta$) if   .

Accepted Answer

The answer of Find f'($\theta$) if   ....

Question 13

A particle moves in a straight line from its initial position so that after t seconds, its distance is given by   feet from its initial position. Find the average velocity of the particle over the interval [1,5] seconds. Use limits to find the instantaneous velocity of the particle at t = 1 seconds.

Accepted Answer

Average velocity = @#IMG-DLM& feet per s

Question 14

Find f '(x) if   .

Accepted Answer

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

Question 15

Let   . Find the slope of the tangent to the graph of f at a general point x0 using limits and find the slope of the tangent line at x0 = 2

Accepted Answer

@#IMG-DLM& The slope

Question 16

If   ,   (Do not reduce any trig ratio identities.)

Accepted Answer

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

Question 17

Let y = x2 + 9. Find the average rate of change of y with respect to x over the interval [-3, -2].

Accepted Answer

Question 18

Find dy/dx if y = cos(sin x).

Accepted Answer

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

Find f '(s) if f(s) = (6s²+ 8)(s² - 7s).

If , find .

y = sin³( $\pi$ - 9 $\theta$ ). Find dy/d $\theta$ .

Given that f(2) = -2 and f '(2) = -2, find an equation for the tangent line to the graph of y = f(x) at the point where x = 2.

An object moves in a straight line so that after t s its distance in mm from its original position is given by s = 3t³ + 4t. Its instantaneous velocity at t = 3s is

Answer true or false. Use a graphing utility to help in obtaining the graph of y = f(x) = |x - 11|. The derivative f '(x) is not defined at x = 11.

Find f '(x) if f(x) = (x⁵ - 11)¹⁰.

If ,

If f(6) = 48, f '(6) = 5, g(6) = 4, g '(6) = -3, find F'(6) if F(x) = .

Find where

Find if .

Find f'( $\theta$ ) if $Find f'( \theta ) if .$ .

A particle moves in a straight line from its initial position so that after t seconds, its distance is given by feet from its initial position. Find the average velocity of the particle over the interval [1,5] seconds. Use limits to find the instantaneous velocity of the particle at t = 1 seconds.

Find f '(x) if .

Let . Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent line at x₀ = 2

If , (Do not reduce any trig ratio identities.)

Let y = x² + 9. Find the average rate of change of y with respect to x over the interval [-3, -2].

Find dy/dx if y = cos(sin x).

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 f '(s) if f(s) = (6s2 + 8)(s2 - 7s).

If , find .

y = sin3( π\piπ - 9 θ\thetaθ ). Find dy/d θ\thetaθ .

Given that f(2) = -2 and f '(2) = -2, find an equation for the tangent line to the graph of y = f(x) at the point where x = 2.

An object moves in a straight line so that after t s its distance in mm from its original position is given by s = 3t3 + 4t. Its instantaneous velocity at t = 3s is

Answer true or false. Use a graphing utility to help in obtaining the graph of y = f(x) = |x - 11|. The derivative f '(x) is not defined at x = 11.

Find f '(x) if f(x) = (x5 - 11)10.

If ,

If f(6) = 48, f '(6) = 5, g(6) = 4, g '(6) = -3, find F'(6) if F(x) = .

Find where

Find if .

Find f'( θ\thetaθ ) if .

A particle moves in a straight line from its initial position so that after t seconds, its distance is given by feet from its initial position. Find the average velocity of the particle over the interval [1,5] seconds. Use limits to find the instantaneous velocity of the particle at t = 1 seconds.

Find f '(x) if .

Let . Find the slope of the tangent to the graph of f at a general point x0 using limits and find the slope of the tangent line at x0 = 2

If , (Do not reduce any trig ratio identities.)

Let y = x2 + 9. Find the average rate of change of y with respect to x over the interval [-3, -2].

Find dy/dx if y = cos(sin x).

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 f '(s) if f(s) = (6s²+ 8)(s² - 7s).

y = sin³( $\pi$ - 9 $\theta$ ). Find dy/d $\theta$ .

An object moves in a straight line so that after t s its distance in mm from its original position is given by s = 3t³ + 4t. Its instantaneous velocity at t = 3s is

Find f '(x) if f(x) = (x⁵ - 11)¹⁰.

Find f'( $\theta$ ) if $Find f'( \theta ) if .$ .

Let . Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent line at x₀ = 2

Let y = x² + 9. Find the average rate of change of y with respect to x over the interval [-3, -2].