Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.2 The Derivative as a Function - Exercises - Page 116: 73


The derivative does not exist at c=0.

Work Step by Step

The derivative of $ f(x) = x^\frac{2}{3}$ is $f'(x) = \frac{2}{3}x^\frac{-1}{3}$, or $\frac{2}{3x^\frac{1}{3}} $ $f'(x)$ is invalid when the denominator is 0. This occurs at the point x (or c) = 0.
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