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: 4


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Work Step by Step

One can see that the function $ f(x)=\frac{x^2}{x^7+1} $ is continuous on $[0,1]$ and $ f(0)=0\neq f(1)=\frac{1}{2}$ and $0.4$ is between $ f(0)$ and $ f(1)$, then by the Intermediate Value Theorem the function $ f(x)$ takes on the value $0.4$ for some $ x\in (0,1)$.
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