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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

(a) If f has a local maximum at (a, b), what can you say about its partial derivatives at (a, b)?

(b) What is a critical point of f?

(a)

To determine

To describe: The partial derivatives at (a,b) if the function f attains local maximum at (a,b) .

Explanation

Let the function be f(x,y) .

The function f(x,y) to have a local maximum at (a,b) , the second partial derivatives of f(x,y) should exist at (a,b) .

That is, the first derivative fx(a,b),fy(a,b) should be 0 and the second order partial derivatives fxx(

(b)

To determine

To describe: The critical point of f.

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Chapter 14 Solutions

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