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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

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If f has a local minimum at (a, b) and f is differentiable at (a, b) then ∇f(a, b) = 0.

To determine

Whether the statement “If f has a local minimum at (a,b) and f is differentiable at (a,b) , then f(a,b)=0 ” is true or false.

Explanation

Theorem used:

If f has a local minimum at (a,b) and the first-order partial derivatives of f exist there, , then fx(a,b)=0 and fy(a,b)=0 .

Reason:

From the theorem, f(x,y) has local minimum and differentiable.

Then, fx(a,b)=0 and fy(a,b)=0 .

The value of f(a,b) is,

f(a,b)=

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Chapter 14 Solutions

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