Explanation Given information: The values of f and its derivatives are given by ( x , y ) f f x f y f x x f y y f x y ( 0 , 0 ) 0 0 0 -2 -3 -2 ( 1 , 0 ) -4 0 0 1 -1 2 ( 0 , 1 ) -6 0 -1 -1 -1 -2 ( − 1 , 0 ) -4 0 0 -1 1 2 ( 0 , − 1 ) -6 1 0 1 -2 1 Definition used: The points where each of the partial derivatives is either zero or undefined are called critical points. Calculation: The critical points are where each of the partial derivatives is either zero or undefined To determine (b) To find: Local minimum , local maximum and saddle points from the critical points.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 8.5, Problem 6P

To determine

(a)

To find:

The critical points of f.

To determine

(b)

To find:

Local minimum, local maximum and saddle points from the critical points.

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Chapter 8.5, Problem 5P

Chapter 8.5, Problem 7P

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Chapter 8 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To find: The critical points of f .

Solution Summary: The author defines critical points as points where each of the partial derivatives is either zero or undefined.

Concept explainers

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(a)

To find:

The critical points of f.

(b)

To find:

Local minimum, local maximum and saddle points from the critical points.

Want to see the full answer?

Chapter 8 Solutions

(a) To find: The critical points of f .

Solution Summary: The author defines critical points as points where each of the partial derivatives is either zero or undefined.

Concept explainers

Videos

(a) To find: The critical points of f.

(b) To find: Local minimum, local maximum and saddle points from the critical points.

Want to see the full answer?

Chapter 8 Solutions

(a)

To find:

The critical points of f.

(b)

To find:

Local minimum, local maximum and saddle points from the critical points.