Calculus: Early Transcendentals 8th Edition

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

Chapter 14 - Review - True-False Quiz - Page 982: 7

Answer

TRUE

Work Step by Step

If $f$ has a local minimum at $(a,b)$, then it is a critical point and therefore has partial derivatives $f_x$ and $f_y = 0$. Since the gradient is $(f_x, f_y)$, the gradient is also $0$. The statement is true.
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