Explanation Given: Function f ( x ) = x 4 − 4 x 3 + 8 x Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. According to the second derivative test: Let us assume a critical point to be p If f ″ ( p ) > 0 , then p is local minimum If f ″ ( p ) < 0 ,then p is local maximum f ″ ( p ) = 0 ,then test tells nothing Calculation: Given function as follows: f ( x ) = x 4 − 4 x 3 + 8 x First derivative is calculated as f ′ ( x ) = 4 x 3 − 4 ( 3 x 2 ) + 8 ( 1 ) f ′ ( x )

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 4.1, Problem 30P

To determine

To find if the critical point x=1 for the below function is a local maximum or local minimum

f(x)=x4−4x3+8x

Expert Solution & Answer

Chapter 4 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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To find if the critical point x = 1 for the below function is a local maximum or local minimum f ( x ) = x 4 − 4 x 3 + 8 x

Solution Summary: The author explains that the critical point x=1 for the below function is a local maximum or local minimum.

Concept explainers

Videos

To find if the critical point x=1 for the below function is a local maximum or local minimum

f(x)=x4−4x3+8x

Chapter 4 Solutions

To find if the critical point x = 1 for the below function is a local maximum or local minimum f ( x ) = x 4 − 4 x 3 + 8 x

Solution Summary: The author explains that the critical point x=1 for the below function is a local maximum or local minimum.

Concept explainers

Videos

To find if the critical point x=1 for the below function is a local maximum or local minimum f(x)=x4−4x3+8x

Chapter 4 Solutions

To find if the critical point x=1 for the below function is a local maximum or local minimum

f(x)=x4−4x3+8x