Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.9 Hyperbolic Functions - Exercises - Page 384: 3


See the details below.

Work Step by Step

Let $y=\sinh x$; then $y'=\cosh x$. Since $\cosh x$ is always positive, then $y=\sinh x$ is always increasing. Now, Let $y=\cosh x$, then $y'=\sinh x$. Since $\sin x=0$ at $x=0$, then we have a critical point $x=0$. Since, $\sinh 1\gt 0$, then $y=\cosh x$ is always increasing for all positive values of $x$ and decreasing for all negative values of $x$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.