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: 92

Answer

Please see below.

Work Step by Step

The function $f(x)=x^4-x^2+3x-1$ is clearly continuous on the closed interval $[0,1]$, and also we have $f(0)=-1<0$ and $f(1)=2>0$. So by applying the Intermediate Value Theorem, there must exist some real number $c$ such that $f(c)=0$. Looking at the graph, we can approximate the root:$$c \approx 0.4 \, .$$By zooming in repeatedly on the graph we can approximate the root much better:$$c \approx 0.37 \, .$$ Using a root calculator, we can find the root more accurately:$$c \approx 0.3733 \, .$$
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