Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.8 Intermediate Value Theorem - Exercises - Page 86: 1


See the proof below.

Work Step by Step

Since the function $ f(x)=x^3+x $ is continuous on $[1,2]$ and $ f(1)=2\neq f(2)=10$ and $9$ is between $ f(1)$ and $f(2)$, then by the Intermediate Value Theorem the function $ f(x)$ takes on the value $9$ for some $ x\in (1,2)$.
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.