Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - Review - True-False Quiz - Page 991: 6

Answer

False

Work Step by Step

False For $F$ to be differentiable at $(a,b)$ is not enough to say that $f_{x}(a, b)$ and $f_{y}(a, b)$ both exist; they must both also be continuous at $(a, b)$. Hence, the statement is false.
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