Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.4 - Tangent Planes and Linear Approximation - 14.4 Exercise: 12

Answer

$L(x,y) = x+1/4y$

Work Step by Step

Question: $f(x,y) = \sqrt {xy}$, $(1,4)$ The equation of the linearization function: $L(x,y) = f(a,b) + f_{x}(a,b)(x - a) + f_{y}(a,b)(y - b)$ $f(1,4) = 2$ $f_{x} = 1/2*\sqrt {xy} * y$ = $y/{2\sqrt {xy}}$ so $f_{x}(1,4) = 1$ $f_{y} = 1/2*\sqrt {xy} * x$ = $x/{2\sqrt {xy}}$ so $f_{y}(1,4) = 1/4$ So the equation is: $L(x,y) = 2 +(x-1) +1/4* (y-4)$ And the final answer is: $L(x,y) = x+1/4y$
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