Explanation Given: c = − 1 , ƒ ( x ) = x 2 + 2 x Formula used: The average rate of change Δ y Δ x = f ( x ) − f ( c ) x − c . Calculation: The average rate of change from c = − 1 to x is. Δ y Δ x = f ( x ) − f ( − 1 ) x − ( − 1 ) =

Mylab Math With Pearson Etext -- Standalone Access Card -- For Precalculus (11th Edition)

11th Edition

ISBN: 9780135189795

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 14.2, Problem 47AYU

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To find: The limit as $x$ approaches $c$ of the average rate of change of the function from $c$ to $x$ .

For, $c = - 1, ƒ (x) = x^{2} + 2 x$ .

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Chapter 14.2, Problem 46AYU

Chapter 14.2, Problem 48AYU

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A graph of the function f is given below: Study the graph of ƒ at the value given below. Select each of the following that applies for the value a = 1 Of is defined at a. If is not defined at x = a. Of is continuous at x = a. If is discontinuous at x = a. Of is smooth at x = a. Of is not smooth at = a. If has a horizontal tangent line at = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. If has no tangent line at x = a. f(a + h) - f(a) lim is finite. h→0 h f(a + h) - f(a) lim h->0+ and lim h h->0- f(a + h) - f(a) h are infinite. lim does not exist. h→0 f(a+h) - f(a) h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

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A graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

Chapter 14 Solutions

Mylab Math With Pearson Etext -- Standalone Access Card -- For Precalculus (11th Edition)

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

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The limit as x approaches c of the average rate of change of the function from c to x . For, c = − 1 , ƒ ( x ) = x 2 + 2 x .

Solution Summary: The author calculates the average rate of change from c = 1 to x.

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To find: The limit as $x$ approaches $c$ of the average rate of change of the function from $c$ to $x$ .

For, $c = - 1, ƒ (x) = x^{2} + 2 x$ .

Want to see the full answer?

Chapter 14 Solutions

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The limit as x approaches c of the average rate of change of the function from c to x . For, c = − 1 , ƒ ( x ) = x 2 + 2 x .

Solution Summary: The author calculates the average rate of change from c = 1 to x.

Concept explainers

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To find: The limit as x approaches c of the average rate of change of the function from c to x . For, c = −1, ƒ( x ) = x 2 + 2x .

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To find: The limit as $x$ approaches $c$ of the average rate of change of the function from $c$ to $x$ .

For, $c = - 1, ƒ (x) = x^{2} + 2 x$ .