a) Suppose that f, g: R3 R are differentiable at a point (a, b, c), and that

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a) Suppose that f, g: R3 †’ R are differentiable at a point (a, b, c), and that f(a, b, c) is an extremum of f subject to the constraint g(x, y, z) = k, where k: is a constant. Prove that

and

b) Use part a) to find all extrema of f(x, y, z) = 4xy + 2xz + 2yz subject to the constraint xyz = 16.

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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Mar 29, 2016 04:23 AM

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a) Suppose that f, g: R3 R are differentiable at a point (a, b, c), and that

Question:

af (a , b. c)-(a, b, c)--(a, b, c)dg. (a, b, c) = 0 ах ag az af ах af :az dg dy ag af ay

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a If g x a b c g y a b c g z a b c 0 then the equations obv...View the full answer

An Introduction to Analysis

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