Explanation Given information: f ( x ) = x 3 − 3 x + 10 Definition used: A point at which the graph of a function f changes concavity is called an inflection point. At the inflection points, f ' ' is zero or undefined. For any function f , a point p in the domain of f where f ' ( p ) = 0 or f ' ( p ) is undefined is called a critical point Of the function. Calculation: f ( x ) = x 3 − 3 x + 10 (Given) f ' ( x ) = 3 x 2 − 3 f ' ' ( x ) = 6 x f ' ( x ) = 0 ⇒ 3 x 2 − 3 = 0 ⇒ 3 ( x 2 − 1 ) = 0 ⇒ ( x 2 − 1 ) = 0 ⇒ x 2 = 1 ⇒ x = ± 1 The critical point is x = − 1 , 1

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.2, Problem 13P

To determine

To find:

The critical point and inflection points of the function f(x)=x3−3x+10 and use the graph to identify each critical point as local maximum, local minimum, or neither.

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Chapter 4.2, Problem 12P

Chapter 4.2, Problem 14P

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Chapter 4 Solutions

APPLIED CALCULUS-WILEYPLUS

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The critical point and inflection points of the function f ( x ) = x 3 − 3 x + 10 and use the graph to identify each critical point as local maximum , local minimum , or neither.

Solution Summary: The author calculates the critical point and inflection points of the function f(x)=x3-3x+10.

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To find:

The critical point and inflection points of the function f(x)=x3−3x+10 and use the graph to identify each critical point as local maximum, local minimum, or neither.

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Chapter 4 Solutions

The critical point and inflection points of the function f ( x ) = x 3 − 3 x + 10 and use the graph to identify each critical point as local maximum , local minimum , or neither.

Solution Summary: The author calculates the critical point and inflection points of the function f(x)=x3-3x+10.

Concept explainers

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To find: The critical point and inflection points of the function f(x)=x3−3x+10 and use the graph to identify each critical point as local maximum, local minimum, or neither.

Want to see the full answer?

Chapter 4 Solutions

To find:

The critical point and inflection points of the function f(x)=x3−3x+10 and use the graph to identify each critical point as local maximum, local minimum, or neither.