Question 1

If   , find   .

Accepted Answer

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

Question 2

Find all x-values on [0, 2 $\pi$] where f(x) is not differentiable. f(x) = cos x cot x

Accepted Answer

A)    
B)  0,  $\pi$, 2 $\pi$ 
C)    
D)  0 
E)  none 
A)    
B)  0,  $\pi$, 2 $\pi$ 
C)    
D)  0 
E)  none

Question 3

Answer true or false. If   ,   .

Accepted Answer

A) True 
 B)False

Question 4

Find f'(x) where f(x) = x2(sin 8x)6.

Accepted Answer

The answer of Find f'(x) where f(x) = x2(sin 8x)6....

Question 5

Show that the parabola y = -x2 and the line x - 10y - 255 = 0 intersect at right angles at one of their points of intersection.

Accepted Answer

For the line, the slope is described by

Question 6

Find the average rate of change of y with respect to x over the interval [2, 7]. y = f(x) = 2x3

Accepted Answer

A)  74 
B)  140 
C)  134 
D)  96 
E)  335 
A)  74 
B)  140 
C)  134 
D)  96 
E)  335

Question 7

A rock is dropped from a height of 828.1 meters and falls toward earth in a straight line. In t seconds the rock drops a distance of 4.9t2 meters. What is the instantaneous velocity downward when it hits the ground?

Accepted Answer

A)  3,360,173.089 meters/s 
B)  127.4 meters/s 
C)  63.7 meters/s 
D)  9.8 meters/s 
E)  26 meters/s 
A)  3,360,173.089 meters/s 
B)  127.4 meters/s 
C)  63.7 meters/s 
D)  9.8 meters/s 
E)  26 meters/s

Question 8

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 9

Find f '(x) where f(x) = (x5 - 3)7(x5 + 2)4.

Accepted Answer

35x⁴(x⁵ - 3)⁶

Question 10

Find f '(x) if f(x) = 2x3 - 3x.

Accepted Answer

A)  6x2 - 3 
B)  6x2 
C)  6x3 - 3 
D)  2x2 - 3 
E)  6x3 
A)  6x2 - 3 
B)  6x2 
C)  6x3 - 3 
D)  2x2 - 3 
E)  6x3

Question 11

Find the instantaneous rate of change of y with respect to x at x0 = 4. y = 4x2 - 8

Accepted Answer

A)  32 
B)  24 
C)  16 
D)  40 
E)  64 
A)  32 
B)  24 
C)  16 
D)  40 
E)  64

Question 12

y = 4x2 + 9x + 2. Find d2y/dx2.

Accepted Answer

A)  8 
B)  8x + 9 
C)  4 
D)  4x + 2 
E)  2 
A)  8 
B)  8x + 9 
C)  4 
D)  4x + 2 
E)  2

Question 13

f(x) = (x4 - 3)38. f '(x) =

Accepted Answer

A)  38x3 (x4 - 3)37 
B)  4x3 (x4 - 3)37 
C)  152x3 (x4 - 3)37 
D)  152(x4 - 3)37 
E)  38(x4 - 3)37 
A)  38x3 (x4 - 3)37 
B)  4x3 (x4 - 3)37 
C)  152x3 (x4 - 3)37 
D)  152(x4 - 3)37 
E)  38(x4 - 3)37

Question 14

Find the x-coordinates of all points in the interval [-2 $\pi$, 2 $\pi$] at which the graph of   has a horizontal tangent line.

Accepted Answer

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

Question 15

Find f '(t) if   .

Accepted Answer

y = t^-1 - 4t

Question 16

Find d6y/dx6 if y = cos x.

Accepted Answer

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

Question 17

Use the definition of the derivative to calculate f '(x) if   and find the equations of the tangent line and the normal line to the graph of f at x = 2.

Accepted Answer

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

Question 18

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 at x0 = 5.

Accepted Answer

@#IMG-DLM& The slope

Question 19

Find d2y/dx2 if y = x tan x.

Accepted Answer

A)  2x tan x sec x 
B)  x sec x 
C)  2 sec 2 x + 2x tan x sec 2 x 
D)  sec x 
E)  -2x tan x sec x 
A)  2x tan x sec x 
B)  x sec x 
C)  2 sec 2 x + 2x tan x sec 2 x 
D)  sec x 
E)  -2x tan x sec x

Question 20

Find   if y = tan x .

Accepted Answer

The answer of Find   if y = tan...

If , find .

Find all x-values on [0, 2 $\pi$ ] where f(x) is not differentiable. f(x) = cos x cot x

Answer true or false. If , .

Find f'(x) where f(x) = x²(sin 8x)⁶.

Show that the parabola y = -x² and the line x - 10y - 255 = 0 intersect at right angles at one of their points of intersection.

Find the average rate of change of y with respect to x over the interval [2, 7]. y = f(x) = 2x³

A rock is dropped from a height of 828.1 meters and falls toward earth in a straight line. In t seconds the rock drops a distance of 4.9t² meters. What is the instantaneous velocity downward when it hits the ground?

Find if .

Find f '(x) where f(x) = (x⁵ - 3)⁷(x⁵ + 2)⁴.

Find f '(x) if f(x) = 2x³ - 3x.

Find the instantaneous rate of change of y with respect to x at x₀ = 4. y = 4x² - 8

y = 4x² + 9x + 2. Find d²y/dx².

f(x) = (x⁴ - 3)³⁸. f '(x) =

Find the x-coordinates of all points in the interval [-2 $\pi$ , 2 $\pi$ ] at which the graph of $Find the x-coordinates of all points in the interval [-2 \pi , 2 \pi ] at which the graph of has a horizontal tangent line.$ has a horizontal tangent line.

Find f '(t) if .

Find d⁶y/dx⁶ if y = cos x.

Use the definition of the derivative to calculate f '(x) if and find the equations of the tangent line and the normal line to the graph of f at x = 2.

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 at x₀ = 5.

Find d²y/dx² if y = x tan x.

Find if y = tan 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