Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 3 - Applications of Differentiation - 3.2 Exercises - Page 176: 75



Work Step by Step

Being a polynomial, $f(x)$ is continuous for all values of $x$ and differentiable at every value of $x$ and hence Rolle's theorem can be applied. Let the three roots be $\alpha, \beta,$ and $\gamma$ such that $\alpha\lt\beta\lt\gamma\to$ Rolle's Theorem guarantees the existence of a horizontal tangent over the interval $[\alpha, \beta]$ and another over the interval $[\beta, \gamma]$.
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