Explanation Given information: f ( x ) = 3 x 5 − 5 x 3 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 ) = 3 x 5 − 5 x 3 (Given) f ' ( x ) = 15 x 4 − 15 x 2 f ' ' ( x ) = 60 x 3 − 30 x f ' ( x ) = 0 ⇒ 15 x 4 − 15 x 2 = 0 ⇒ 15 x 2 ( x 2 − 1 ) = 0 ⇒ x 2 ( x 2 − 1 ) = 0 ⇒ x 2 ( x + 1 ) ( x − 1 ) = 0 ⇒ x = 0 , − 1 , 1 The criticalpoints are x = 0 , − 1 , 1

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 4.2, Problem 21P

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To find:

The critical point and inflection points of the function f(x)=3x5−5x3 and use the graph to identify each critical point as local maximum, local minimum, or neither.

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Chapter 4.2, Problem 20P

Chapter 4.2, Problem 22P

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The critical point and inflection points of the function f ( x ) = 3 x 5 − 5 x 3 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)=3x5-5.

Concept explainers

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To find:

The critical point and inflection points of the function f(x)=3x5−5x3 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

The critical point and inflection points of the function f ( x ) = 3 x 5 − 5 x 3 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)=3x5-5.

Concept explainers

Videos

To find: The critical point and inflection points of the function f(x)=3x5−5x3 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)=3x5−5x3 and use the graph to identify each critical point as local maximum, local minimum, or neither.