Answer
$$L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(y-b).$$
Work Step by Step
The linearization of $f(x,y)$ at $(a,b)$ is defined by $$L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(y-b).$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 15 - Differentiation in Several Variables - 15.4 Differentiability and Tangent Planes - Preliminary Questions - Page 788: 1
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