Explanation Given: f ( 1 ) = 5 ; f ′ ( 1 ) = 0 ; f ″ ( 1 ) = − 2 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 < To determine (b) To sketch the graph near critical point and label the coordinates of critical point

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.1, Problem 26P

To determine

(a)

To find if the critical point is a local maximum or local minimum

f(1)=5;f′(1)=0;f″(1)=−2

To determine

(b)

To sketch the graph near critical point and label the coordinates of critical point

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Chapter 4.1, Problem 25P

Chapter 4.1, Problem 27P

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Chapter 4 Solutions

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(a) To find if the critical point is a local maximum or local minimum f ( 1 ) = 5 ; f ′ ( 1 ) = 0 ; f ″ ( 1 ) = − 2

Solution Summary: The author explains how to find if the critical point is a local maximum or local minimum.

Concept explainers

Videos

(a)

To find if the critical point is a local maximum or local minimum

f(1)=5;f′(1)=0;f″(1)=−2

(b)

To sketch the graph near critical point and label the coordinates of critical point

Want to see the full answer?

Chapter 4 Solutions

(a) To find if the critical point is a local maximum or local minimum f ( 1 ) = 5 ; f ′ ( 1 ) = 0 ; f ″ ( 1 ) = − 2

Solution Summary: The author explains how to find if the critical point is a local maximum or local minimum.

Concept explainers

Videos

(a) To find if the critical point is a local maximum or local minimum f(1)=5;f′(1)=0;f″(1)=−2

(b) To sketch the graph near critical point and label the coordinates of critical point

Want to see the full answer?

Chapter 4 Solutions

(a)

To find if the critical point is a local maximum or local minimum

f(1)=5;f′(1)=0;f″(1)=−2

(b)

To sketch the graph near critical point and label the coordinates of critical point