Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - True-False Quiz: 22

Answer

This is true.

Work Step by Step

At every point that the function is differentiable (where the derivative exists) the function is continuous as well. The function is continuous at $x=r$ if $\lim_{x\to r}f(x)=f(r)$. Thus if $f'(r)$ exists then $\lim_{x\to r}f(x)=f(r)$.
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