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 - Page 80: 88

Answer

Check work for explanation.

Work Step by Step

Since $f(x)$ is a polynomial, it is continuous for all values of $x.$ $f(0)=(0)^3+5(0)-3=-3\to f(0)\lt0.$ $f(1)=(1)^3+5(1)-3=3\to f(1)\gt0$ Since $f(x)$ is continuous over the interval $[0, 1]$ and the sign of $f(x)$ changes over the interval $[0, 1]$, then the Intermediate Value Theorem guarantees at least one root in the interval.
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