Approximate by applying Newton's Method to the equation x2 - 5 = 0. Use 2 for your initial value and calculate three iterations.

A) 2.2360680 B) 2.2359480 C) 2.2360560 D) 2.236111 E) 2.25 A) 2.2360680 B) 2.2359480 C) 2.2360560 D) 2.236111 E) 2.25

A storm is passing with the wind speed in mph changing over time according to v(t) = -t2 + 22t - 96, for 0 $\le$ t $\le$10. Find the highest wind speed that occurs.

A) 267 mph B) 217 mph C) 459 mph D) 41 mph E) 25 mph A) 267 mph B) 217 mph C) 459 mph D) 41 mph E) 25 mph

Approximate by applying Newton's Method to the equation x3 - 11 = 0. Use 2.5 for your initial value and calculate four iterations.

A) 2.5 B) 2.253333 C) 2.2243608 D) 2.2239800 E) 2.22398009 A) 2.5 B) 2.253333 C) 2.2243608 D) 2.2239800 E) 2.22398009

Find the value for which f(x) = x3- 4 on [2, 6] satisfies the Mean-Value Theorem.

A) 3.830 B) 3.055 C) 7.211 D) 4.163 E) 5.099 A) 3.830 B) 3.055 C) 7.211 D) 4.163 E) 5.099

Exam 4: The Derivative in Graphing and Applications

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-3, 3]? If so, find all values of C that satisfy the conclusion of the theorem.

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(Essay)

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Question 1

Correct Answer:

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No, since f is not differentiable at x = 0 which is in (-3, 3).

Determine which function is graphed.

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(Multiple Choice)

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Question 2

Correct Answer:

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Find the relative extrema for f(x) = 3x⁵ -4x⁴.

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Question 3

Correct Answer:

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Relative maximum at Relative minimum at

The position function of a particle is given by s = t(t -2)² for t $\ge$ 0. Find the functions for v and a.

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Question 4

Find all relative extrema of f(x) = (x + 2)² - 4.

(Short Answer)

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Question 5

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

(Essay)

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Question 6

Sketch the graph of y = 3 + (x -4)^1/3. Find any stationary points and any inflections points.

(Essay)

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Question 7

Find the relative extreme values for on the interval [-8, 8] and determine where those values occur.

(Essay)

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Question 8

Answer true or false. $Answer true or false. has a relative maximum on (0, \infty ).$ has a relative maximum on (0, $\infty$ ).

(True/False)

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Question 9

Approximate by applying Newton's Method to the equation x² - 5 = 0. Use 2 for your initial value and calculate three iterations.

(Multiple Choice)

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Question 10

If f(x) = 4x⁴ - 5x³ + 19 , find the intervals where f is concave up and where f is concave down.

(Essay)

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Question 11

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

(Essay)

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Question 12

A storm is passing with the wind speed in mph changing over time according to v(t) = -t² + 22t - 96, for 0 $\le$ t $\le$ 10. Find the highest wind speed that occurs.

(Multiple Choice)

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Question 13

The rational function has

(Multiple Choice)

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Question 14

Approximate by applying Newton's Method to the equation x³ - 11 = 0. Use 2.5 for your initial value and calculate four iterations.

(Multiple Choice)

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Question 15

Answer true or false. The rational function has no vertical asymptote.

(True/False)

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Question 16

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x² - 11)² on (- $\infty$ , $\infty$ ), if it exists.

(Multiple Choice)

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Question 17

Sketch a continuous curve having the following properties. f(0) = 4, f(-2) = f(2) = 0; f '(x) > 0 for (- $\infty$ ,0) and f '(x) < 0 for (0, + $\infty$ ), f'(x) < 0 for (- $\infty$ , + $\infty$ ). $Sketch a continuous curve having the following properties. f(0) = 4, f(-2) = f(2) = 0; f '(x) > 0 for (- \infty ,0) and f '(x) < 0 for (0, + \infty ), f'(x) < 0 for (- \infty , + \infty ).$

(Essay)

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Question 18

Answer true or false. An object that is thrown upward and reaches a height of s(t) = 60 + 160t -16t² for 0 $\le$ t $\le$ 3. The object is highest at t = 4.

(True/False)

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Question 19

Find the value for which f(x) = x³- 4 on [2, 6] satisfies the Mean-Value Theorem.

(Multiple Choice)

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Question 20

Showing 1 - 20 of 656

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-3, 3]? If so, find all values of C that satisfy the conclusion of the theorem.

Determine which function is graphed.

Find the relative extrema for f(x) = 3x⁵ -4x⁴.

The position function of a particle is given by s = t(t -2)² for t $\ge$ 0. Find the functions for v and a.

Find all relative extrema of f(x) = (x + 2)² - 4.

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 y = 3 + (x -4)^1/3. Find any stationary points and any inflections points.

Find the relative extreme values for on the interval [-8, 8] and determine where those values occur.

Answer true or false. $Answer true or false. has a relative maximum on (0, \infty ).$ has a relative maximum on (0, $\infty$ ).

Approximate by applying Newton's Method to the equation x² - 5 = 0. Use 2 for your initial value and calculate three iterations.

If f(x) = 4x⁴ - 5x³ + 19 , find the intervals where f is concave up and where f is concave down.

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

A storm is passing with the wind speed in mph changing over time according to v(t) = -t² + 22t - 96, for 0 $\le$ t $\le$ 10. Find the highest wind speed that occurs.

The rational function has

Approximate by applying Newton's Method to the equation x³ - 11 = 0. Use 2.5 for your initial value and calculate four iterations.

Answer true or false. The rational function has no vertical asymptote.

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x² - 11)² on (- $\infty$ , $\infty$ ), if it exists.

Answer true or false. An object that is thrown upward and reaches a height of s(t) = 60 + 160t -16t² for 0 $\le$ t $\le$ 3. The object is highest at t = 4.

Find the value for which f(x) = x³- 4 on [2, 6] satisfies the Mean-Value Theorem.

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

Does satisfy the hypothesis of the Mean-Value Theorem over the interval [-3, 3]? If so, find all values of C that satisfy the conclusion of the theorem.

Determine which function is graphed.

Find the relative extrema for f(x) = 3x5 -4x4.

The position function of a particle is given by s = t(t -2)2 for t ≥\ge≥ 0. Find the functions for v and a.

Find all relative extrema of f(x) = (x + 2)2 - 4.

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 y = 3 + (x -4)1/3. Find any stationary points and any inflections points.

Find the relative extreme values for on the interval [-8, 8] and determine where those values occur.

Answer true or false. has a relative maximum on (0, ∞\infty∞ ).

Approximate by applying Newton's Method to the equation x2 - 5 = 0. Use 2 for your initial value and calculate three iterations.

If f(x) = 4x4 - 5x3 + 19 , find the intervals where f is concave up and where f is concave down.

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

A storm is passing with the wind speed in mph changing over time according to v(t) = -t2 + 22t - 96, for 0 ≤\le≤ t ≤\le≤ 10. Find the highest wind speed that occurs.

The rational function has

Approximate by applying Newton's Method to the equation x3 - 11 = 0. Use 2.5 for your initial value and calculate four iterations.

Answer true or false. The rational function has no vertical asymptote.

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x2 - 11)2 on (- ∞\infty∞ , ∞\infty∞ ), if it exists.

Sketch a continuous curve having the following properties. f(0) = 4, f(-2) = f(2) = 0; f '(x) > 0 for (- ∞\infty∞ ,0) and f '(x) < 0 for (0, + ∞\infty∞ ), f'(x) < 0 for (- ∞\infty∞ , + ∞\infty∞ ).

Answer true or false. An object that is thrown upward and reaches a height of s(t) = 60 + 160t -16t2 for 0 ≤\le≤ t ≤\le≤ 3. The object is highest at t = 4.

Find the value for which f(x) = x3- 4 on [2, 6] satisfies the Mean-Value Theorem.

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

Find the relative extrema for f(x) = 3x⁵ -4x⁴.

The position function of a particle is given by s = t(t -2)² for t $\ge$ 0. Find the functions for v and a.

Find all relative extrema of f(x) = (x + 2)² - 4.

Sketch the graph of y = 3 + (x -4)^1/3. Find any stationary points and any inflections points.

Answer true or false. $Answer true or false. has a relative maximum on (0, \infty ).$ has a relative maximum on (0, $\infty$ ).

Approximate by applying Newton's Method to the equation x² - 5 = 0. Use 2 for your initial value and calculate three iterations.

If f(x) = 4x⁴ - 5x³ + 19 , find the intervals where f is concave up and where f is concave down.

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

A storm is passing with the wind speed in mph changing over time according to v(t) = -t² + 22t - 96, for 0 $\le$ t $\le$ 10. Find the highest wind speed that occurs.

Approximate by applying Newton's Method to the equation x³ - 11 = 0. Use 2.5 for your initial value and calculate four iterations.

Use a graphing utility to assist in determining the location of the absolute maximum of f(x) = -(x² - 11)² on (- $\infty$ , $\infty$ ), if it exists.

Answer true or false. An object that is thrown upward and reaches a height of s(t) = 60 + 160t -16t² for 0 $\le$ t $\le$ 3. The object is highest at t = 4.

Find the value for which f(x) = x³- 4 on [2, 6] satisfies the Mean-Value Theorem.