University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Questions to Guide Your Review - Page 275: 12

Answer

See the explanation below.

Work Step by Step

A point on the graph at which the slope of a function $f(x)$ approaches $\infty$ from one side and $-\infty$ from the other side is defined as a cusp on the graph. For Example: $f(x)=x^{2/3}$ at $x=0 \\ \implies f'(x)=\dfrac{2}{3x^{1/3}} $ Therefore, we have: $\lim\limits_{x \to 0^{+}}f'(x) =+\infty \\ \lim\limits_{x \to 0^{-}}f'(x) =-\infty$
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