Question 1

Answer true or false. f(x) =   has a critical point.

Accepted Answer

A) True 
 B)False

Question 2

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 6 $\pi$ s that is given by 4cos(4t). Find the maximum current produced.

Accepted Answer

A)  4A 
B)  0A 
C)  2 $\pi$A 
D)    A 
E)    A 
A)  4A 
B)  0A 
C)  2 $\pi$A 
D)    A 
E)    A

Question 3

If f(x) = (x - 7)4 + 8 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 4

Use Newton's Method to find the largest positive solution of x5 + 5x3 -8x2 - 6 = 0.

Accepted Answer

A)  2.3902439 
B)  1.9412059 
C)  1.6510083 
D)  1.6508863 
E)  1.6509963 
A)  2.3902439 
B)  1.9412059 
C)  1.6510083 
D)  1.6508863 
E)  1.6509963

Question 5

For a triangle with sides 7 m, 24 m, and 25 m, the smallest circle that contains the triangle has a diameter of

Accepted Answer

A)  7 m 
B)  24 m 
C)  25 m 
D)  31 m 
E)  28 m 
A)  7 m 
B)  24 m 
C)  25 m 
D)  31 m 
E)  28 m

Question 6

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft2. If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Accepted Answer

Let x and y be the dimensions shown in t

Question 7

Use a graphing utility to graph f(x) =   . How many points of inflection does the function have?

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  3 
E)  4 
A)  0 
B)  1 
C)  2 
D)  3 
E)  4

Question 8

The product of 2 positive numbers is 768. 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 9

Find the relative extrema for f(x) = 3x - sin 2x, 0 < x <  $\pi$.

Accepted Answer

f '(x) = 3 - 2 cos 2x
Critical

Question 10

If f(x) = 5x4 - 17x3 + 45 , find the intervals where f is increasing and where f is decreasing.

Accepted Answer

Increasing

Question 11

Given the position function s = 5t3 - 30t2 + 6t + 10; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

Accepted Answer

v = 15t² - 60t + 6

Question 12

A company has a cost of operation function given by C(t) = 0.05t2 -2t + 500 for 0 $\le$ t $\le$500. Find the minimum cost of operation.

Accepted Answer

A)  660 
B)  560 
C)  1,120 
D)  499.90 
E)  539 
A)  660 
B)  560 
C)  1,120 
D)  499.90 
E)  539

Question 13

Use Newton's Method to find the largest positive solution of x4 - 8x2 - 9 = 0. Use 4 for your initial value and calculate eight iterations.

Accepted Answer

A)  3.380208 
B)  3.0000000 
C)  3.0799923 
D)  3.0045383 
E)  3.0000157 
A)  3.380208 
B)  3.0000000 
C)  3.0799923 
D)  3.0045383 
E)  3.0000157

Question 14

If f(x) = x(x -21)2 , find the inflection points.

Accepted Answer

The answer of If f(x) = x(x -21)2 , find...

Question 15

The equation, x3 -x2 -3x - 2 = 0 has one real solution for 1 < x < 2. Approximate it by Newton's Method.

Accepted Answer

f(x) = x³-x

Question 16

If f(x) = 4x4 - 13x3 , find the location of any inflection points.

Accepted Answer

The answer of If f(x) = 4x4 - 13x3 ,...

Question 17

Answer true or false. If f ''(-2) = -4 and f ''(2) = 4, then there must be an inflection point on (-2, 2).

Accepted Answer

A) True 
 B)False

Question 18

Use a graphing utility to estimate the absolute minimum of f(x) = x6e x on [-1, 1].

Accepted Answer

Question 19

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 4 $\pi$ s that is given by 2cos(3t). Find the maximum current produced.

Accepted Answer

A)  2A 
B)  0A 
C)  2 $\pi$A 
D)    A 
E)    A 
A)  2A 
B)  0A 
C)  2 $\pi$A 
D)    A 
E)    A

Question 20

Given   . Find any extrema and any inflection points.

Accepted Answer

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

Answer true or false. f(x) = has a critical point.

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 6 $\pi$ s that is given by 4cos(4t). Find the maximum current produced.

If f(x) = (x - 7)⁴ + 8 , find the intervals where f is increasing and where f is decreasing.

Use Newton's Method to find the largest positive solution of x⁵ + 5x³ -8x² - 6 = 0.

For a triangle with sides 7 m, 24 m, and 25 m, the smallest circle that contains the triangle has a diameter of

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft². If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Use a graphing utility to graph f(x) = . How many points of inflection does the function have?

The product of 2 positive numbers is 768. Find the numbers, if the sum of one number and the cube of the other is to be minimum.

Find the relative extrema for f(x) = 3x - sin 2x, 0 < x < $\pi$ .

If f(x) = 5x⁴ - 17x³ + 45 , find the intervals where f is increasing and where f is decreasing.

Given the position function s = 5t³ - 30t² + 6t + 10; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

A company has a cost of operation function given by C(t) = 0.05t² -2t + 500 for 0 $\le$ t $\le$ 500. Find the minimum cost of operation.

Use Newton's Method to find the largest positive solution of x⁴ - 8x² - 9 = 0. Use 4 for your initial value and calculate eight iterations.

If f(x) = x(x -21)² , find the inflection points.

The equation, x³ -x²-3x - 2 = 0 has one real solution for 1 < x < 2. Approximate it by Newton's Method.

If f(x) = 4x⁴ - 13x³ , find the location of any inflection points.

Answer true or false. If f ''(-2) = -4 and f ''(2) = 4, then there must be an inflection point on (-2, 2).

Use a graphing utility to estimate the absolute minimum of f(x) = x⁶e ^x on [-1, 1].

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 4 $\pi$ s that is given by 2cos(3t). Find the maximum current produced.

Given . Find any extrema and any inflection points.

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

Answer true or false. f(x) = has a critical point.

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 6 π\piπ s that is given by 4cos(4t). Find the maximum current produced.

If f(x) = (x - 7)4 + 8 , find the intervals where f is increasing and where f is decreasing.

Use Newton's Method to find the largest positive solution of x5 + 5x3 -8x2 - 6 = 0.

For a triangle with sides 7 m, 24 m, and 25 m, the smallest circle that contains the triangle has a diameter of

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft2. If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Use a graphing utility to graph f(x) = . How many points of inflection does the function have?

The product of 2 positive numbers is 768. Find the numbers, if the sum of one number and the cube of the other is to be minimum.

Find the relative extrema for f(x) = 3x - sin 2x, 0 < x < π\piπ .

If f(x) = 5x4 - 17x3 + 45 , find the intervals where f is increasing and where f is decreasing.

Given the position function s = 5t3 - 30t2 + 6t + 10; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

A company has a cost of operation function given by C(t) = 0.05t2 -2t + 500 for 0 ≤\le≤ t ≤\le≤ 500. Find the minimum cost of operation.

Use Newton's Method to find the largest positive solution of x4 - 8x2 - 9 = 0. Use 4 for your initial value and calculate eight iterations.

If f(x) = x(x -21)2 , find the inflection points.

The equation, x3 -x2 -3x - 2 = 0 has one real solution for 1 < x < 2. Approximate it by Newton's Method.

If f(x) = 4x4 - 13x3 , find the location of any inflection points.

Answer true or false. If f ''(-2) = -4 and f ''(2) = 4, then there must be an inflection point on (-2, 2).

Use a graphing utility to estimate the absolute minimum of f(x) = x6e x on [-1, 1].

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 4 π\piπ s that is given by 2cos(3t). Find the maximum current produced.

Given . Find any extrema and any inflection points.

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

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 6 $\pi$ s that is given by 4cos(4t). Find the maximum current produced.

If f(x) = (x - 7)⁴ + 8 , find the intervals where f is increasing and where f is decreasing.

Use Newton's Method to find the largest positive solution of x⁵ + 5x³ -8x² - 6 = 0.

A rectangular garden is to be laid out with one side adjoining a neighbor's lot and is to contain 507ft². If the neighbor agrees to pay for half the dividing fence, what should the dimensions of the garden be to insure a minimum cost of enclosure?

Find the relative extrema for f(x) = 3x - sin 2x, 0 < x < $\pi$ .

If f(x) = 5x⁴ - 17x³ + 45 , find the intervals where f is increasing and where f is decreasing.

Given the position function s = 5t³ - 30t² + 6t + 10; find s and v when a = 0 (Where v is the velocity and a is the acceleration.).

A company has a cost of operation function given by C(t) = 0.05t² -2t + 500 for 0 $\le$ t $\le$ 500. Find the minimum cost of operation.

Use Newton's Method to find the largest positive solution of x⁴ - 8x² - 9 = 0. Use 4 for your initial value and calculate eight iterations.

If f(x) = x(x -21)² , find the inflection points.

The equation, x³ -x²-3x - 2 = 0 has one real solution for 1 < x < 2. Approximate it by Newton's Method.

If f(x) = 4x⁴ - 13x³ , find the location of any inflection points.

Use a graphing utility to estimate the absolute minimum of f(x) = x⁶e ^x on [-1, 1].

An electrical generator produces a current in amperes starting at t = 0 s and running until t = 4 $\pi$ s that is given by 2cos(3t). Find the maximum current produced.