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 - 3.2 Exercises: 74

Answer

False.

Work Step by Step

No information was given about the nature of $f(x)$ and hence if $f(x)$ is not continuous over the interval, it does not necessarily have $2$ horizontal tangent lines. For example $\tan{x}$ has infinitely many x-intercepts but no horizontal tangents lines since $\tan{x}$ is not continuous at $x=\frac{k}{2}\pi$ where $ k$ is any integer.
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