Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - Review - True-False Quiz: 20

Answer

False.

Work Step by Step

There is a condition missing if we want to apply the Intermediate Value Theorem, f must also be continuous for this to be true. Construct a piecewise function, such as $f(x)=\left\{\begin{array}{lll} 1, & & x < 2\\ -1 & & x \geq 2 \end{array}\right.$ which fits the conditions of the statement, but there is no c in the interval [1,3] for which f(c)=0.
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