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: 95

Answer

$c=3.$

Work Step by Step

Since $f(x)$ is a polynomial, it is continuous for all values of $x.$ $f(0)=(0)^2+0-1=-1.$ $f(5)=(5)^2+5-1=29.$ Since f(x) is continuous and $-1\lt 11\lt29,$ then there exists a value $c$ in the interval $[0, 5]$ such that $f(c)=11.$ $x^2+x-1=11\to x^2+x-12=0\to$ $(x+4)(x-3)\to x=-4$ (rejected; not in interval) or $x=3.$ $c=3.$
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