Question 1

Use a graphing utility to generate the graph of f(x) = x4 - 14x3 + 29x2 -36x + 2, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

Accepted Answer

A)  There is a relative maximum at x = 9. 
B)  There is a relative minimum at x = 0. 
C)  There is a relative maximum at x = 0. 
D)  There is a relative minimum at x = 9. 
E)  There are no relative extrema.

Question 2

Approximate by applying Newton's Method to the equation x² -44 = 0. Use 6 for your initial value and calculate five iterations.

Accepted Answer

The answer of Approximate  by applying Newton's Method to...

Question 3

The derivative of a continuous function is  . Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

Accepted Answer

The answer of The derivative of a continuous function is...

Question 4

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

Accepted Answer

The answer of Sketch the graph of  . Find...

Question 5

On a [-10, 10] by [-10, 10] window on a graphing utility the rational function  has

Accepted Answer

A)  one horizontal asymptote; no vertical asymptote 
B)  no horizontal asymptote; one vertical asymptote 
C)  one horizontal asymptote; two vertical asymptote 
D)  one horizontal asymptote; three vertical asymptotes 
E)  one horizontal asymptote; one vertical asymptotes

Question 6

f(x) = |7 - 6x| has an absolute minimum of

Accepted Answer

A)  7 
B)  6 
C)  -35 
D)  -42 
E)  0

Question 7

The largest open interval over which f is concave up for  is

Accepted Answer

A)  (2, $\infty$) 
B)  (-$\infty$, 2) 
C)  (-$\infty$, $\infty$) 
D)  (-2, 2) 
E)  nowhere

Question 8

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x3 - 2x and y = x4 + 4x - 4.

Accepted Answer

A)  1.4314065 
B)  1.5496529 
C)  1.4142136 
D)  1.8453125 
E)  2.3253012

Question 9

Find the relative extrema for f(x) = x^2/3(3 - x).

Accepted Answer

The answer of Find the relative extrema for f(x) =...

Question 10

Find the point on the curve x² + y² = 121 closest to (10, 0).

Accepted Answer

The answer of Find the point on the curve x²...

Question 11

Find the relative extrema for f(x) = x¹⁰^/⁹ -10x^-1^/⁹.

Accepted Answer

The answer of Find the relative extrema for f(x) =...

Question 12

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁵ + 3

Accepted Answer

The answer of Find the value of c in the...

Question 13

Verify that  satisfies the hypothesis of the Mean-Value Theorem over the interval [3, 5] and find all values of C that satisfy the conclusion of the theorem.

Accepted Answer

The answer of Verify that  satisfies the hypothesis of...

Question 14

f(x) = |x -5| has

Accepted Answer

A)  a relative minimum at x = 0 
B)  a relative maximum at x = 0 
C)  a relative maximum at x = 5 
D)  a relative minimum at x = 5 
E)  a relative minimum at x = -5

Question 15

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Accepted Answer

The answer of A sheet of cardboard 30 in square...

Question 16

Use Newton's Method to find the greatest x-coordinate of the intersection of y = 8x4-19x2 and y = 11x2 - 89.

Accepted Answer

A)  2.3526499 
B)  3.2462874 
C)  1.7428006 
D)  3.9475724 
E)  3.0442692

Question 17

The position function of a particle is given by s(t) = t⁷- 5t + 11. Find the acceleration when t = 3.

Accepted Answer

The answer of The position function of a particle is...

Question 18

Answer true or false. f(x) = sin 4x cos 4x on  has an absolute maximum at  .

Accepted Answer

A) True 
 B)False

Question 19

Approximate by applying Newton's Method to the equation x³ - 73 = 0. Use 4 for your initial value and calculate five iterations.

Accepted Answer

The answer of Approximate  by applying Newton's Method to...

Question 20

Answer true or false. Using a graphing utility it can be shown that f(x) = x4 sin 5x has a relative maximum on 0 < x < 2 $\pi$.

Accepted Answer

A) True 
 B)False

Exam 4: The Derivative in Graphing and Applications

Use a graphing utility to generate the graph of f(x) = x⁴ - 14x³ + 29x² -36x + 2, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

Approximate by applying Newton's Method to the equation x² -44 = 0. Use 6 for your initial value and calculate five iterations.

The derivative of a continuous function is . Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

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

On a [-10, 10] by [-10, 10] window on a graphing utility the rational function has

f(x) = |7 - 6x| has an absolute minimum of

The largest open interval over which f is concave up for $The largest open interval over which f is concave up for is A) (2, \infty ) B) (- \infty , 2) C) (- \infty , \infty ) D) (-2, 2) E) nowhere$ is

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x³ - 2x and y = x⁴ + 4x - 4.

Find the relative extrema for f(x) = x^2/3(3 - x).

Find the point on the curve x² + y² = 121 closest to (10, 0).

Find the relative extrema for f(x) = x¹⁰^/⁹ -10x^-1^/⁹.

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁵ + 3

Verify that satisfies the hypothesis of the Mean-Value Theorem over the interval [3, 5] and find all values of C that satisfy the conclusion of the theorem.

f(x) = |x -5| has

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Use Newton's Method to find the greatest x-coordinate of the intersection of y = 8x⁴-19x² and y = 11x² - 89.

The position function of a particle is given by s(t) = t⁷- 5t + 11. Find the acceleration when t = 3.

Answer true or false. f(x) = sin 4x cos 4x on has an absolute maximum at .

Approximate by applying Newton's Method to the equation x³ - 73 = 0. Use 4 for your initial value and calculate five iterations.

Answer true or false. Using a graphing utility it can be shown that f(x) = x⁴ sin 5x has a relative maximum on 0 < x < 2 $\pi$ .

Exam 4: The Derivative in Graphing and Applications

Use a graphing utility to generate the graph of f(x) = x4 - 14x3 + 29x2 -36x + 2, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

Approximate by applying Newton's Method to the equation x2 -44 = 0. Use 6 for your initial value and calculate five iterations.

The derivative of a continuous function is . Find all critical points and determine whether a relative maximum, relative minimum or neither occurs there.

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

On a [-10, 10] by [-10, 10] window on a graphing utility the rational function has

f(x) = |7 - 6x| has an absolute minimum of

The largest open interval over which f is concave up for is

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x3 - 2x and y = x4 + 4x - 4.

Find the relative extrema for f(x) = x2/3(3 - x).

Find the point on the curve x2 + y2 = 121 closest to (10, 0).

Find the relative extrema for f(x) = x10/9 -10x-1/9.

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x5 + 3

Verify that satisfies the hypothesis of the Mean-Value Theorem over the interval [3, 5] and find all values of C that satisfy the conclusion of the theorem.

f(x) = |x -5| has

A sheet of cardboard 30 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

Use Newton's Method to find the greatest x-coordinate of the intersection of y = 8x4-19x2 and y = 11x2 - 89.

The position function of a particle is given by s(t) = t7- 5t + 11. Find the acceleration when t = 3.

Answer true or false. f(x) = sin 4x cos 4x on has an absolute maximum at .

Approximate by applying Newton's Method to the equation x3 - 73 = 0. Use 4 for your initial value and calculate five iterations.

Answer true or false. Using a graphing utility it can be shown that f(x) = x4 sin 5x has a relative maximum on 0 < x < 2 π\piπ .

Use a graphing utility to generate the graph of f(x) = x⁴ - 14x³ + 29x² -36x + 2, then determine the x-coordinates of all relative extrema on (-10, 10) and identify them as relative maxima or relative minima.

Approximate by applying Newton's Method to the equation x² -44 = 0. Use 6 for your initial value and calculate five iterations.

The largest open interval over which f is concave up for $The largest open interval over which f is concave up for is A) (2, \infty ) B) (- \infty , 2) C) (- \infty , \infty ) D) (-2, 2) E) nowhere$ is

Use Newton's Method to approximate the greatest x-coordinate of the intersection of y = x³ - 2x and y = x⁴ + 4x - 4.

Find the relative extrema for f(x) = x^2/3(3 - x).

Find the point on the curve x² + y² = 121 closest to (10, 0).

Find the relative extrema for f(x) = x¹⁰^/⁹ -10x^-1^/⁹.

Find the value of c in the interval [0, 1] that satisfies the Mean Value Theorem. f(x) = x⁵ + 3

Use Newton's Method to find the greatest x-coordinate of the intersection of y = 8x⁴-19x² and y = 11x² - 89.

The position function of a particle is given by s(t) = t⁷- 5t + 11. Find the acceleration when t = 3.

Approximate by applying Newton's Method to the equation x³ - 73 = 0. Use 4 for your initial value and calculate five iterations.

Answer true or false. Using a graphing utility it can be shown that f(x) = x⁴ sin 5x has a relative maximum on 0 < x < 2 $\pi$ .