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: 29

Answer

Over the specified interval, the function has an absolute maximum equal to $3$ and an absolute minimum equal to $-1.$

Work Step by Step

Using the rule ($\dfrac{d}{dx}|z(x)|=z'(x)\times\dfrac{|z(x)|}{z(x)}$) $\to$ $y'=-\dfrac{|t-3|}{t-3}.$ $y'$ is undefined for $t=3$ which is in the specified interval; hence, $t=3$, along with the interval's endpoints, are possible candidates for an absolute extremum. $y(-1)=-1.$ $y(3)=3.$ $y(5)=1.$ Over the specified interval, the function has an absolute maximum equal to $3$ and an absolute minimum equal to $-1.$
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