Question 1

Find an equation for the tangent line to the curve y = x4 - 11 at (2, 5).

Accepted Answer

A)  y = 32x 
B)  y = 32x - 11 
C)  y = 32x3 - 59 
D)  y = 32x - 59 
E)  y = 32x3 - 11 
A)  y = 32x 
B)  y = 32x - 11 
C)  y = 32x3 - 59 
D)  y = 32x - 59 
E)  y = 32x3 - 11

Question 2

Answer true or false. The magnitude of the instantaneous velocity is always less than the magnitude of the average velocity.

Accepted Answer

A) True 
 B)False

Question 3

Find the instantaneous rate of change of f(x) = -2x2 - 3x + 11 at x0 = 4.

Accepted Answer

Question 4

Answer true or false. If a rock is thrown straight upward to a height of 25 feet from the ground, when it returns to earth its average velocity will be its initial velocity.

Accepted Answer

A) True 
 B)False

Question 5

Answer true or false. If y = cos(x6), d2y/dx2 = -cos(x6).

Accepted Answer

A) True 
 B)False

Question 6

Answer true or false. The slope of the tangent line to the graph of f(x) = 2x2 - 1 at x0 = 5 is 19.

Accepted Answer

A) True 
 B)False

Question 7

If f(3) = 4, f '(3) = -5, g(3) = 2, g '(3) = -4, find F'(3) if F(x) = 2f(x) - g(x) .

Accepted Answer

The answer of If f(3) = 4, f '(3) =...

Question 8

f(x) = 3x cot x. Find f '(x).

Accepted Answer

The answer of f(x) = 3x cot x. Find f...

Question 9

f(x) = x2 cos x + sin x. Find f '(x).

Accepted Answer

-x<sup>2</

Question 10

Find the equation of the tangent line to y = f(x) = 4x at x = 5.

Accepted Answer

A)  y = 4x - 5 
B)  y = 4x 
C)  y = -4x 
D)  y = 4x + 5 
E)  y = 4x - 20 
A)  y = 4x - 5 
B)  y = 4x 
C)  y = -4x 
D)  y = 4x + 5 
E)  y = 4x - 20

Question 11

The figure shows the position versus time curve for a certain particle moving along a straight line. Estimate, from the graph, the instantaneous velocity at 8.

Accepted Answer

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

Question 12

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 13

Answer true or false. A graphing utility can be used to determine that   is differentiable at x = 0.

Accepted Answer

A) True 
 B)False

Question 14

Find f '($\theta$) where f($\theta$) = cos2(6$\theta$6 - $\theta$)6.

Accepted Answer

The answer of Find f '($\theta$) where f($\theta$) = cos2(6$\theta$6...

Question 15

The volume of a sphere is given by   where D is the diameter of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of V with respect to D when D = 2.

Accepted Answer

The instantaneous ra

Question 16

Find the instantaneous rate of change of   at x0 = 2.

Accepted Answer

Question 17

Find the instantaneous rate of change of y with respect to x at x0 = 49.

Accepted Answer

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

Question 18

Use the definition of the derivative to calculate f '(x) if   .

Accepted Answer

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

Question 19

Find   if y = -8x10 .

Accepted Answer

Question 20

Show that the parabola y = x2 and the line x + 6y - 57 = 0 intersect at right angles at one of their points of intersection.

Accepted Answer

For the line, the slope is described by

Find an equation for the tangent line to the curve y = x⁴ - 11 at (2, 5).

Answer true or false. The magnitude of the instantaneous velocity is always less than the magnitude of the average velocity.

Find the instantaneous rate of change of f(x) = -2x² - 3x + 11 at x₀ = 4.

Answer true or false. If a rock is thrown straight upward to a height of 25 feet from the ground, when it returns to earth its average velocity will be its initial velocity.

Answer true or false. If y = cos(x⁶), d²y/dx² = -cos(x⁶).

Answer true or false. The slope of the tangent line to the graph of f(x) = 2x² - 1 at x₀ = 5 is 19.

If f(3) = 4, f '(3) = -5, g(3) = 2, g '(3) = -4, find F'(3) if F(x) = 2f(x) - g(x) .

f(x) = 3x cot x. Find f '(x).

f(x) = x² cos x + sin x. Find f '(x).

Find the equation of the tangent line to y = f(x) = 4x at x = 5.

The figure shows the position versus time curve for a certain particle moving along a straight line. Estimate, from the graph, the instantaneous velocity at 8.

Find if .

Answer true or false. A graphing utility can be used to determine that is differentiable at x = 0.

Find f '( $\theta$ ) where f( $\theta$ ) = cos²(6 $\theta$ ⁶ - $\theta$ )⁶.

The volume of a sphere is given by where D is the diameter of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of V with respect to D when D = 2.

Find the instantaneous rate of change of at x₀ = 2.

Find the instantaneous rate of change of y with respect to x at x₀ = 49.

Use the definition of the derivative to calculate f '(x) if .

Find if y = -8x¹⁰ .

Show that the parabola y = x² and the line x + 6y - 57 = 0 intersect at right angles at one of their points of intersection.

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 an equation for the tangent line to the curve y = x4 - 11 at (2, 5).

Answer true or false. The magnitude of the instantaneous velocity is always less than the magnitude of the average velocity.

Find the instantaneous rate of change of f(x) = -2x2 - 3x + 11 at x0 = 4.

Answer true or false. If a rock is thrown straight upward to a height of 25 feet from the ground, when it returns to earth its average velocity will be its initial velocity.

Answer true or false. If y = cos(x6), d2y/dx2 = -cos(x6).

Answer true or false. The slope of the tangent line to the graph of f(x) = 2x2 - 1 at x0 = 5 is 19.

If f(3) = 4, f '(3) = -5, g(3) = 2, g '(3) = -4, find F'(3) if F(x) = 2f(x) - g(x) .

f(x) = 3x cot x. Find f '(x).

f(x) = x2 cos x + sin x. Find f '(x).

Find the equation of the tangent line to y = f(x) = 4x at x = 5.

The figure shows the position versus time curve for a certain particle moving along a straight line. Estimate, from the graph, the instantaneous velocity at 8.

Find if .

Answer true or false. A graphing utility can be used to determine that is differentiable at x = 0.

Find f '( θ\thetaθ ) where f( θ\thetaθ ) = cos2(6 θ\thetaθ 6 - θ\thetaθ )6.

The volume of a sphere is given by where D is the diameter of the sphere. Use the method of Section 3.2 to find the instantaneous rate of change of V with respect to D when D = 2.

Find the instantaneous rate of change of at x0 = 2.

Find the instantaneous rate of change of y with respect to x at x0 = 49.

Use the definition of the derivative to calculate f '(x) if .

Find if y = -8x10 .

Show that the parabola y = x2 and the line x + 6y - 57 = 0 intersect at right angles at one of their points of intersection.

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 an equation for the tangent line to the curve y = x⁴ - 11 at (2, 5).

Find the instantaneous rate of change of f(x) = -2x² - 3x + 11 at x₀ = 4.

Answer true or false. If y = cos(x⁶), d²y/dx² = -cos(x⁶).

Answer true or false. The slope of the tangent line to the graph of f(x) = 2x² - 1 at x₀ = 5 is 19.

f(x) = x² cos x + sin x. Find f '(x).

Find f '( $\theta$ ) where f( $\theta$ ) = cos²(6 $\theta$ ⁶ - $\theta$ )⁶.

Find the instantaneous rate of change of at x₀ = 2.

Find the instantaneous rate of change of y with respect to x at x₀ = 49.

Find if y = -8x¹⁰ .

Show that the parabola y = x² and the line x + 6y - 57 = 0 intersect at right angles at one of their points of intersection.