Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - Concept Check: 9

Answer

The Intermediate Value Theorem: Suppose that - $f$ is continuous on the closed interval $[a, b]$ - let $N$ be any number between $f(a)$ and $f(b)$, $f(a)\ne f(b)$ then there exists a number $c$ in $(a,b)$ such that $f(c)=N$

Work Step by Step

The Intermediate Value Theorem: Suppose that - $f$ is continuous on the closed interval $[a, b]$ - let $N$ be any number between $f(a)$ and $f(b)$, $f(a)\ne f(b)$ then there exists a number $c$ in $(a,b)$ such that $f(c)=N$ You can check the theorem in the Continuity section. This theorem can be intuitively thought as true as follows: - N is a number between $f(a)$ and $f(b)$ - We draw a horizontal line $y=N$ - If the graph has no break, then it must intersect the horizontal line $y=N$ at a point $c$ between $a$ and $b$.
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