Answer
False
Work Step by Step
False.
Example:
$f(x) = x^{1/3}$
$f(0) = 0$
$f'(x) = \frac{1}{3\sqrt[3] x^2}$
$f'(0) = \frac{1}{3\sqrt[3] {(0)}^2}=\frac{1}{0}$ Does not exist.
Hence, it is continuous at $x=0$ but not differentiable.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 2 - Differentiation - 2.1 Exercises - Page 105: 94
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
