Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - Review Exercises: 63


Check work for proof.

Work Step by Step

Since $f(x)$ is a polynomial, it is continuous for all values of $x.$ $f(1)=2(1)^3-3=-1\to f(1)\lt0.$ $f(2)=2(2)^3-3=13\to f(2)\gt0.$ Since $f(x)$ is continuous over the interval $[1, 2]$ and the sign of $f(x)$ changes over the interval $[1, 2]$, then the Intermediate Value Theorem guarantees at least one zero in the interval.
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.