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: 9


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Work Step by Step

Let $f(x)= x ^2.$ Note that $f$ is continuous on $\left[0 ,2\right]$ with $f(0)=0$ and $f(2)=4 .$ Therefore, by the IVT, there is a $c \in\left[0,2\right]$ such that $f(c)= c^2=2 .$ Thus the equation $x^2=2$ has a solution $c$ in $\left[0,2\right]$.
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