Explanation Given: g ( − 5 ) = 4 ; g ′ ( − 5 ) = 0 ; g ″ ( − 5 ) = 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 ,then test tells nothing Cal To determine (b) To sketch the graph near critical point and label the coordinates of critical point

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.1, Problem 27P

To determine

(a)

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

g(−5)=4;g′(−5)=0;g″(−5)=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 26P

Chapter 4.1, Problem 28P

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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(a) To find if the critical point is a local maximum or local minimum g ( − 5 ) = 4 ; g ′ ( − 5 ) = 0 ; g ″ ( − 5 ) = 2

Solution Summary: The author explains that critical points are the points where the function is defined and its derivative is undefined or zero.

Concept explainers

Videos

(a)

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

g(−5)=4;g′(−5)=0;g″(−5)=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 g ( − 5 ) = 4 ; g ′ ( − 5 ) = 0 ; g ″ ( − 5 ) = 2

Solution Summary: The author explains that critical points are the points where the function is defined and its derivative is undefined or zero.

Concept explainers

Videos

(a) To find if the critical point is a local maximum or local minimum g(−5)=4;g′(−5)=0;g″(−5)=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

g(−5)=4;g′(−5)=0;g″(−5)=2

(b)

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