Explanation Given information: f ( x ) = 2 x 3 + 3 x 2 − 36 x + 5 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 ) = 2 x 3 + 3 x 2 − 36 x + 5 (Given) f ' ( x ) = 6 x 2 + 6 x − 36 f ' ' ( x ) = 12 x + 6 f ' ( x ) = 0 ⇒ 6 x 2 + 6 x − 36 = 0 ⇒ 6 ( x 2 + x − 6 ) = 0 ⇒ x 2 + x − 6 = 0 ⇒ ( x + 3 ) ( x − 2 ) = 0 ⇒ x = − 3 , 2 The critical points are x = − 3 , 2

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.2, Problem 14P

To determine

To find:

The critical point and inflection points of the function f(x)=2x3+3x2−36x+5 and use the graph to identify each critical point as local maximum, local minimum, or neither.

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Chapter 4.2, Problem 13P

Chapter 4.2, Problem 15P

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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 ) = 2 x 3 + 3 x 2 − 36 x + 5 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 and inflection points of the function f(x)=2x3+3

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To find:

The critical point and inflection points of the function f(x)=2x3+3x2−36x+5 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 ) = 2 x 3 + 3 x 2 − 36 x + 5 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 and inflection points of the function f(x)=2x3+3

Concept explainers

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To find: The critical point and inflection points of the function f(x)=2x3+3x2−36x+5 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)=2x3+3x2−36x+5 and use the graph to identify each critical point as local maximum, local minimum, or neither.