Question 1

Let f(x) = 2x . Estimate f '(2) using a graphing utility.

Accepted Answer

The answer of Let f(x) = 2x . Estimate f...

Question 2

A 16 foot long ladder leans against a wall at an angle $\theta$ with the horizontal as shown in the figure. The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate at which x changes with $\theta$when $\theta$ = 45°. Express the answer in units of feet/degree.

Accepted Answer

The answer of A 16 foot long ladder leans against...

Question 3

Answer true or false. If an object is thrown straight upward with an instantaneous velocity of 20 m/s, its instantaneous velocity at the point where it stops rising is 0.

Accepted Answer

A) True 
 B)False

Question 4

Find equations for the tangent and normal lines to the graph of f(x) = x cos 6x at x =  $\pi$/6.

Accepted Answer

Tangent: y

Question 5

Use the definition of the derivative to calculate f '(x) if f(x) = 5x2 - 8x + 6.

Accepted Answer

The answer of Use the definition of the derivative to...

Question 6

Use a graphing utility to locate all horizontal tangent lines to the curve y = x3 + 3x2 + 12.

Accepted Answer

A)  x = 0 
B)  x = -3 and x = 0 
C)  x = -2 and x = 0 
D)  x = -2 
E)  x = -3 
A)  x = 0 
B)  x = -3 and x = 0 
C)  x = -2 and x = 0 
D)  x = -2 
E)  x = -3

Question 7

Find the instantaneous rate of change of   with respect to x at a general point x0.

Accepted Answer

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

Question 8

Let   . Use the definition of the derivative to find   .

Accepted Answer

The answer of Let   . Use the definition...

Question 9

Let   . Find the average rate of change of y with respect to x over the given interval [3,4].

Accepted Answer

The answer of Let   . Find the average...

Question 10

Find f ''(2) if   .

Accepted Answer

f '(x) = @#IMG-DLM&

Question 11

Find the x-coordinate of the point on the graph of y = x4 + 4 where the tangent line is parallel to the secant line that cuts the curve at x = 2 and at x = 3.

Accepted Answer

A)    
B)  85 
C)  20 
D)    
E)    
A)    
B)  85 
C)  20 
D)    
E)

Question 12

Given   , find   .

Accepted Answer

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

Question 13

Answer true or false. Given f '(x) = 5x and   , then   if F(x) = f(g(x)).

Accepted Answer

A) True 
 B)False

Question 14

Answer true or false. If f(x) = cos x sec x - sin x, f '(x) = 1 - cos x.

Accepted Answer

A) True 
 B)False

Question 15

If y = x6 cos x, find d2y/dx2.

Accepted Answer

A)  30x4 cos x - 12x5 sin x + x6 cos x 
B)  30x4 cos x - 6x5 sin x - x6 cos x 
C)  30x4 cos x - 12x5 sin x - x6 cos x 
D)  30x4 cos x - 12x5 sin x 
E)  6x5 cos x - x6 sin x 
A)  30x4 cos x - 12x5 sin x + x6 cos x 
B)  30x4 cos x - 6x5 sin x - x6 cos x 
C)  30x4 cos x - 12x5 sin x - x6 cos x 
D)  30x4 cos x - 12x5 sin x 
E)  6x5 cos x - x6 sin x

Question 16

Let y = x2 + 12. Find the instantaneous rate of change of y with respect to x at the point x = -1 .

Accepted Answer

Question 17

Find f '(x) if f(x) = (7x4 + 9) cos x.

Accepted Answer

28x<sup>3</sup> cos

Question 18

Find f '(t) where   .

Accepted Answer

The answer of Find f '(t) where   ....

Question 19

An airplane is flying on a horizontal path at a height of 6000ft, as shown in the figure. At what rate is the distance s between the airplane and the fixed point P changing with $\theta$when $\theta$ = 20°. Express the answer in units of feet/degree.

Accepted Answer

The answer of An airplane is flying on a horizontal...

Question 20

f(x) = 4 cos x + 7 sin x. Find f'(x).

Accepted Answer

f ' (x) =

Let f(x) = 2^x . Estimate f '(2) using a graphing utility.

Answer true or false. If an object is thrown straight upward with an instantaneous velocity of 20 m/s, its instantaneous velocity at the point where it stops rising is 0.

Find equations for the tangent and normal lines to the graph of f(x) = x cos 6x at x = $\pi$ /6.

Use the definition of the derivative to calculate f '(x) if f(x) = 5x² - 8x + 6.

Use a graphing utility to locate all horizontal tangent lines to the curve y = x³ + 3x² + 12.

Find the instantaneous rate of change of with respect to x at a general point x₀.

Let . Use the definition of the derivative to find .

Let . Find the average rate of change of y with respect to x over the given interval [3,4].

Find f ''(2) if .

Find the x-coordinate of the point on the graph of y = x⁴ + 4 where the tangent line is parallel to the secant line that cuts the curve at x = 2 and at x = 3.

Given , find .

Answer true or false. Given f '(x) = 5x and , then if F(x) = f(g(x)).

Answer true or false. If f(x) = cos x sec x - sin x, f '(x) = 1 - cos x.

If y = x⁶ cos x, find d²y/dx².

Let y = x² + 12. Find the instantaneous rate of change of y with respect to x at the point x = -1 .

Find f '(x) if f(x) = (7x⁴ + 9) cos x.

Find f '(t) where .

f(x) = 4 cos x + 7 sin x. Find f'(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

Let f(x) = 2x . Estimate f '(2) using a graphing utility.

Answer true or false. If an object is thrown straight upward with an instantaneous velocity of 20 m/s, its instantaneous velocity at the point where it stops rising is 0.

Find equations for the tangent and normal lines to the graph of f(x) = x cos 6x at x = π\piπ /6.

Use the definition of the derivative to calculate f '(x) if f(x) = 5x2 - 8x + 6.

Use a graphing utility to locate all horizontal tangent lines to the curve y = x3 + 3x2 + 12.

Find the instantaneous rate of change of with respect to x at a general point x0.

Let . Use the definition of the derivative to find .

Let . Find the average rate of change of y with respect to x over the given interval [3,4].

Find f ''(2) if .

Find the x-coordinate of the point on the graph of y = x4 + 4 where the tangent line is parallel to the secant line that cuts the curve at x = 2 and at x = 3.

Given , find .

Answer true or false. Given f '(x) = 5x and , then if F(x) = f(g(x)).

Answer true or false. If f(x) = cos x sec x - sin x, f '(x) = 1 - cos x.

If y = x6 cos x, find d2y/dx2.

Let y = x2 + 12. Find the instantaneous rate of change of y with respect to x at the point x = -1 .

Find f '(x) if f(x) = (7x4 + 9) cos x.

Find f '(t) where .

An airplane is flying on a horizontal path at a height of 6000ft, as shown in the figure. At what rate is the distance s between the airplane and the fixed point P changing with θ\thetaθ when θ\thetaθ = 20°. Express the answer in units of feet/degree.

f(x) = 4 cos x + 7 sin x. Find f'(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

Let f(x) = 2^x . Estimate f '(2) using a graphing utility.

Find equations for the tangent and normal lines to the graph of f(x) = x cos 6x at x = $\pi$ /6.

Use the definition of the derivative to calculate f '(x) if f(x) = 5x² - 8x + 6.

Use a graphing utility to locate all horizontal tangent lines to the curve y = x³ + 3x² + 12.

Find the instantaneous rate of change of with respect to x at a general point x₀.

Find the x-coordinate of the point on the graph of y = x⁴ + 4 where the tangent line is parallel to the secant line that cuts the curve at x = 2 and at x = 3.

If y = x⁶ cos x, find d²y/dx².

Let y = x² + 12. Find the instantaneous rate of change of y with respect to x at the point x = -1 .

Find f '(x) if f(x) = (7x⁴ + 9) cos x.