University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 4 - Section 4.1 - Extreme Values of Functions - Exercises - Page 216: 64

Answer

$y$ has no maximum or minimum values at all.

Work Step by Step

$$y=e^x-e^{-x}$$ 1) Find all the critical points of the function: - Find $y'$: $$y'=e^x(x)'-e^{-x}(-x)'$$ $$y'=e^x+e^{-x}$$ - As both $e^x$ and $e^{-x}$ are $\gt0$ for all $x$, there is no value of $x$ for which $y'=0$ - There is also no value of $x$ for which $y'$ is not defined. So function $y$ has no critical points. 2) Since function $y$ has no critical points and there are also no predefined domains to have the endpoints, we can conclude that $y$ has no maximum or minimum values at all. This can be seen in the graph of $y$, which is a constantly increasing curve as $x$ increases rightward.
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