Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 4: Applications of Derivatives - Section 4.1 - Extreme Values of Functions - Exercises 4.1 - Page 192: 72

Answer

See explanations.

Work Step by Step

Step 1. If a function has no endpoints, this means that its domain should be $(-\infty, \infty)$ Step 2. If a function $f$ has no critical points, this means that it is differentiable in the domain and $f'(x)\ne0$. Step 3. We can find examples that $f'(x)=constant\ne0$, such as $f(x)=2x$ which satisfy the conditions. In this case, there will not be any extrema for the function.
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