College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Review Exercises - Page 398: 39

Answer

See below.

Work Step by Step

The Intermediate Value Theorem says that if a continuous (polynomials are always continuous) function on an interval [a,b] takes values $f(a)$ and $f(b)$ at the endpoints, then the function takes all values between $f(a)$ and $f(b)$ at some point of the interval. Evaluate the function at the endpoints. $f(0)=3\cdot0^3-0-1=0-0-1=-1.$ $f(1)=3\cdot1^3-1-1=3-1-1=1.$ Since $-1\lt0\lt1$, according to the Intermediate Value Theorem, there must be a $0$ in the given interval.
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