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 4.2 - The Mean Value Theorem - Exercises 4.2 - Page 198: 27

Answer

Yes

Work Step by Step

The Roll's Theorem states that there is a point $c$ taken as a constant when the function $f(x)$ is differentiable with $f'(x)=0$. This means that $f'(c)=\dfrac{f(b)-f(a)}{b-a} \ne 0$, which contradicts to $f'(x)=0$ for all $x$. Thus, we have when $f(x)=3$ then $f'(x)=0$ for all $x$.So, this might be saying true for when $f(x)=f(-1)=3$ for all $x$.
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.