Explanation Given information: f ( x ) = x 4 − 2 x 2 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 4 − 2 x 2 (Given) f ' ( x ) = 4 x 3 − 4 x f ' ' ( x ) = 12 x 2 − 4 f ' ( x ) = 0 ⇒ 4 x 3 − 4 x = 0 ⇒ 4 x ( x 2 − 1 ) = 0 ⇒ x ( x 2 − 1 ) = 0 ⇒ x ( x + 1 ) ( x − 1 ) = 0 ⇒ x = 0 , − 1 , 1 The criticalpoints are x = 0 , − 1 , 1

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 4.2, Problem 16P

To determine

To find:

The critical point and inflection points of the function f(x)=x4−2x2 and use the graph to identify each critical point as local maximum, local minimum, or neither.

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Chapter 4.2, Problem 15P

Chapter 4.2, Problem 17P

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Chapter 4 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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The critical point and inflection points of the function f ( x ) = x 4 − 2 x 2 and use the graph to identify each critical point as local maximum , local minimum , or neither.

Solution Summary: The author explains how to find the critical point and inflection points of the function f(x)=x42.

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To find:

The critical point and inflection points of the function f(x)=x4−2x2 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 4 − 2 x 2 and use the graph to identify each critical point as local maximum , local minimum , or neither.

Solution Summary: The author explains how to find the critical point and inflection points of the function f(x)=x42.

Concept explainers

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To find: The critical point and inflection points of the function f(x)=x4−2x2 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)=x4−2x2 and use the graph to identify each critical point as local maximum, local minimum, or neither.