Calculus (3rd Edition)

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

Chapter 2 - Limits - Chapter Review Exercises - Page 96: 73


The IVT guarantees there exists a $c \in(0,1)$ such that $$f(c)=2^{-c^{2}}-c=0$$

Work Step by Step

Let $$f(x)=2^{-x^{2}}-x .$$ Observe that $f$ is continuous on $[0,1]$ with $$f(0)=2^{0}-0=1\gt0$$ and $$f(1)= 2^{-1}-1\lt 0 .$$ Therefore, the IVT guarantees that there exists a $c \in(0,1)$ such that $$f(c)=2^{-c^{2}}-c=0$$
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.