Calculus 10th Edition

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

Chapter 1 - Limits and Their Properties - 1.4 Exercises: 87


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Work Step by Step

Since $f(x)$ is a polynomial, it is continuous for all values of $x.$ $f(1)=\frac{1}{12}(1)^4-(1)^3+4=\dfrac{37}{12}\to f(1)\gt0.$ $f(2)=\frac{1}{12}(2)^4-(2)^3+4=-\dfrac{8}{3}\to f(2)\lt0.$ Since $f(x)$ is continuous over the interval $[1, 2]$ and the sign of $f(x)$ changes over the interval $[1, 2]$, then the Intermediate Value Theorem guarantees at least one root in the interval.
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