Question 1

Use a graphing utility to determine where   is decreasing on [0, 2 $\pi$].

Accepted Answer

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

Question 2

Given   . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative maximum at @#IMG-DLM& Inflect

Question 3

Approximate   by applying Newton's Method to the equation x3 - 10 = 0.

Accepted Answer

A)  2 
B)  2.166667 
C)  2.1545036 
D)  2.1544345 
E)  2.15443469 
A)  2 
B)  2.166667 
C)  2.1545036 
D)  2.1544345 
E)  2.15443469

Question 4

Answer true or false. The Mean-Value Theorem can be used on f(x) = |x - 2| on [-4, 4].

Accepted Answer

A) True 
 B)False

Question 5

Find the relative extreme values for f(x) = |10 -5x| on the interval [-4, 4] and determine where those values occur.

Accepted Answer

@#IMG-DLM& ; @#IMG-DLM& ; f '(x) does not exist at

Question 6

The position function of a particle is given by s(t) = t4 - 3t + 8. Find the acceleration when t = 2.

Accepted Answer

v(t) = 4t³

Question 7

Answer true or false. The rectangle with the largest area that can be drawn inside a semi-circle is a square.

Accepted Answer

A) True 
 B)False

Question 8

Use Newton's Method to find the largest positive solution of x4 + x3 - 6x - 6 = 0. Use 4 for your initial value and calculate eight iterations.

Accepted Answer

A)  1.8381538 
B)  1.9835930 
C)  1.8171206 
D)  2.3659571 
E)  3.0268456 
A)  1.8381538 
B)  1.9835930 
C)  1.8171206 
D)  2.3659571 
E)  3.0268456

Question 9

Find the dimensions of the rectangular area of maximum area which can be laid out within a triangle of base 24 and altitude 6 if one side of the rectangle lies on the base of the triangle.

Accepted Answer

Let x and y be as shown in the

Question 10

If f(x) = 4x4 - 72x2 , find the location of any inflection points.

Accepted Answer

The answer of If f(x) = 4x4 - 72x2 ,...

Question 11

Answer true or false. If f '(x) < 0 for all x on the interval I, then f(x) is concave down on the interval I.

Accepted Answer

A) True 
 B)False

Question 12

The product of 2 positive numbers is 1,875. Find the numbers, if the sum of one number and the cube of the other is to be minimum.

Accepted Answer

Let x = one positive number and y = the

Question 13

Find the extreme values for f(x) = x - sin 3x on the interval   and determine where those values occur.

Accepted Answer

f '(x) = 1 - 3 cos 3x ; Critic

Question 14

If f(x) = (x - 5)4 + 1 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 15

Sketch a continuous curve y = f(x) for x > 0 if   = 0, and f '(x) =   for all x > 0. Is the curve concave up or concave down?

Accepted Answer

The curve

Question 16

If f(x) = 15x4 -10x3 + 1 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

The answer of If f(x) = 15x4 -10x3 + 1...

Question 17

Sketch the graph of   . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative maximum a

Question 18

Given   . Find any stationary points and any inflection points.

Accepted Answer

@#IMG-DLM& @#IMG-DLM& Relative

Question 19

If f(x) = 3x4 - 19x3 , find the location of any inflection points.

Accepted Answer

The answer of If f(x) = 3x4 - 19x3 ,...

Question 20

If f(x) = x(x + 4)3 , find the intervals where f is concave up and where f is concave down.

Accepted Answer

Use a graphing utility to determine where $Use a graphing utility to determine where is decreasing on [0, 2 \pi ].$ is decreasing on [0, 2 $\pi$ ].

Given . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Approximate by applying Newton's Method to the equation x³ - 10 = 0.

Answer true or false. The Mean-Value Theorem can be used on f(x) = |x - 2| on [-4, 4].

Find the relative extreme values for f(x) = |10 -5x| on the interval [-4, 4] and determine where those values occur.

The position function of a particle is given by s(t) = t⁴ - 3t + 8. Find the acceleration when t = 2.

Answer true or false. The rectangle with the largest area that can be drawn inside a semi-circle is a square.

Use Newton's Method to find the largest positive solution of x⁴ + x³ - 6x - 6 = 0. Use 4 for your initial value and calculate eight iterations.

Find the dimensions of the rectangular area of maximum area which can be laid out within a triangle of base 24 and altitude 6 if one side of the rectangle lies on the base of the triangle.

If f(x) = 4x⁴ - 72x²_,find the location of any inflection points.

Answer true or false. If f '(x) < 0 for all x on the interval I, then f(x) is concave down on the interval I.

The product of 2 positive numbers is 1,875. Find the numbers, if the sum of one number and the cube of the other is to be minimum.

Find the extreme values for f(x) = x - sin 3x on the interval and determine where those values occur.

If f(x) = (x - 5)⁴ + 1 , find the intervals where f is increasing and where f is decreasing.

Sketch a continuous curve y = f(x) for x > 0 if = 0, and f '(x) = for all x > 0. Is the curve concave up or concave down?

If f(x) = 15x⁴ -10x³ + 1 , find the intervals where f is concave up and where f is concave down.

Sketch the graph of . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.

Given . Find any stationary points and any inflection points.

If f(x) = 3x⁴ - 19x³ , find the location of any inflection points.

If f(x) = x(x + 4)³ , find the intervals where f is concave up and where f is concave down.

Limits and Continuity

The Derivative

Topics in Deifferentiation

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 4: The Derivative in Graphing and Applications

Use a graphing utility to determine where is decreasing on [0, 2 π\piπ ].

Given . Find any stationary points and any points of inflection. Also find any vertical and horizontal asymptotes.

Approximate by applying Newton's Method to the equation x3 - 10 = 0.

Answer true or false. The Mean-Value Theorem can be used on f(x) = |x - 2| on [-4, 4].

Find the relative extreme values for f(x) = |10 -5x| on the interval [-4, 4] and determine where those values occur.

The position function of a particle is given by s(t) = t4 - 3t + 8. Find the acceleration when t = 2.

Answer true or false. The rectangle with the largest area that can be drawn inside a semi-circle is a square.

Use Newton's Method to find the largest positive solution of x4 + x3 - 6x - 6 = 0. Use 4 for your initial value and calculate eight iterations.

Find the dimensions of the rectangular area of maximum area which can be laid out within a triangle of base 24 and altitude 6 if one side of the rectangle lies on the base of the triangle.

If f(x) = 4x4 - 72x2 , find the location of any inflection points.

Answer true or false. If f '(x) < 0 for all x on the interval I, then f(x) is concave down on the interval I.

The product of 2 positive numbers is 1,875. Find the numbers, if the sum of one number and the cube of the other is to be minimum.

Find the extreme values for f(x) = x - sin 3x on the interval and determine where those values occur.

If f(x) = (x - 5)4 + 1 , find the intervals where f is increasing and where f is decreasing.

Sketch a continuous curve y = f(x) for x > 0 if = 0, and f '(x) = for all x > 0. Is the curve concave up or concave down?

If f(x) = 15x4 -10x3 + 1 , find the intervals where f is concave up and where f is concave down.

Sketch the graph of . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.

Given . Find any stationary points and any inflection points.

If f(x) = 3x4 - 19x3 , find the location of any inflection points.

If f(x) = x(x + 4)3 , find the intervals where f is concave up and where f is concave down.

Limits and Continuity

The Derivative

Topics in Deifferentiation

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

Use a graphing utility to determine where $Use a graphing utility to determine where is decreasing on [0, 2 \pi ].$ is decreasing on [0, 2 $\pi$ ].

Approximate by applying Newton's Method to the equation x³ - 10 = 0.

The position function of a particle is given by s(t) = t⁴ - 3t + 8. Find the acceleration when t = 2.

Use Newton's Method to find the largest positive solution of x⁴ + x³ - 6x - 6 = 0. Use 4 for your initial value and calculate eight iterations.

If f(x) = 4x⁴ - 72x²_,find the location of any inflection points.

If f(x) = (x - 5)⁴ + 1 , find the intervals where f is increasing and where f is decreasing.

If f(x) = 15x⁴ -10x³ + 1 , find the intervals where f is concave up and where f is concave down.

If f(x) = 3x⁴ - 19x³ , find the location of any inflection points.

If f(x) = x(x + 4)³ , find the intervals where f is concave up and where f is concave down.