Calculus 10th Edition

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

Chapter 3 - Differentiation - 3.2 Exercises: 6

Answer

$f'(x)=0$ for $x=-3.$

Work Step by Step

$f(x)=x^2+6x=x(x+6)\to$ The intercepts are $x=0$ and $x=-6.$ Applying Rolle's Theorem over the interval $[-6, 0]$ guarantees the existence of at least one value $c$ such that $-6\lt c\lt 0$ and $f'(c)=0.$ $f'(x)=2x+6\to f'(x)=0\to 2x+6=0\to c=-3.$
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