Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - True-False Quiz: 16

Answer

The statement is false.

Work Step by Step

The statement follows the result of the Intermediate Value Theorem, which states that let $N$ be any number between $f(a)$ and $f(b)$ and $f(a)\ne f(b)$, then there exists a number $c$ in $(a,b)$ such that $f(c)=N$. However, the Intermediate Value Theorem can only be applied when the function $f(x)$ is continuous on interval $[a,b]$. In this case, we are not sure whether function $f(x)$ is continuous on interval $[1,3]$ or not. It only proves that $f(1)\ne f(3)$, since $f(1)\gt0$ and $f(3)\lt0$ Therefore, the statement is inadequate and false as a result.
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