Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 3 - Applications of Differentiation - 3.1 Exercises: 6


$f'(0)$ is undefined.

Work Step by Step

Using the rule that $\dfrac{d}{dx}|z(x)|=z'(x)\dfrac{|z(x)|}{z(x)}\to$ $f'(x)=0-(1\times\dfrac{|x|}{x})=-\dfrac{|x|}{x}; x\ne0.$ $f'(0)$ is undefined because the left-side limit of +1 does not agree with the right-hand limit of -1. This can also be seen from the graph.
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