Explanation Given information: f ( x ) = x 5 − 5 x 4 + 35 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 5 − 5 x 4 + 35 (Given) f ' ( x ) = 5 x 4 − 20 x 3 f ' ' ( x ) = 20 x 3 − 60 x 2 f ' ( x ) = 0 ⇒ 5 x 4 − 20 x 3 = 0 ⇒ 5 x 3 ( x − 4 ) = 0 ⇒ x 3 ( x − 4 ) = 0 ⇒ x = 0 , 4 The criticalpoints are x = 0 , 4

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.2, Problem 20P

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The critical point and inflection points of the function f(x)=x5−5x4+35 and use the graph to identify each critical point as local maximum, local minimum, or neither.

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Chapter 4.2, Problem 19P

Chapter 4.2, Problem 21P

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

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The critical point and inflection points of the function f ( x ) = x 5 − 5 x 4 + 35 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)=x5-54+35.

Concept explainers

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To find:

The critical point and inflection points of the function f(x)=x5−5x4+35 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 5 − 5 x 4 + 35 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)=x5-54+35.

Concept explainers

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To find: The critical point and inflection points of the function f(x)=x5−5x4+35 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)=x5−5x4+35 and use the graph to identify each critical point as local maximum, local minimum, or neither.