Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - Review - True-False Quiz: 2

Answer

false

Work Step by Step

Given: $f_{x}=x+y^{2}$ and $f_{y}=x-y^{2}$ Take second derivative of the function with respect to $y$ keeping $x$ constant. $f_{xy}=1$ $f_{y}=x-y^{2}$ Take second derivative of the function with respect to $x$ keeping $y$ constant. $f_{yx}=2y$ Thus, $f_{xy} \ne f_{yx}$ Thus , the second derivative of the function f does not verified the Clairaut's Theorem, that is, $f_{xy} = f_{yx}$ Hence, the statement is false.
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