Calculus 10th Edition

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

Chapter 3 - Applications of Differentiation - 3.1 Exercises: 22

Answer

Over the specified interval, the function has an absolute maximum equal to $36$ and an absolute minimum equal to $-4.$

Work Step by Step

$f'(x)=6x^2-6=6(x-1)(x+1).$ $f'(x)$ is defined for all x in the interval. $f'(x)=0\to x=1$ or $x=-1$ but only $x=1$ is in the specified interval. The function could attain an absolute extremum at $x=1$ or at the interval endpoints. $f(0)=0.$ $f(1)=-4.$ $f(3)=36.$ Over the specified interval, the function has an absolute maximum equal to $36$ and an absolute minimum equal to $-4.$
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