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: 2

Answer

$f'(0)=0$ and $f'(2)=0.$

Work Step by Step

Using the chain rule with $u=\frac{\pi}{2}x\to \dfrac{du}{dx}=\frac{\pi}{2}.$ $f'(x)=-\sin{\frac{\pi x}{2}}\times\frac{\pi}{2}=-\frac{\pi}{2}\sin{\frac{\pi x}{2}}.$ $f'(0)=-\frac{\pi}{2}\sin{\frac{\pi(0)}{2}}=0.$ $f'(2)=-\frac{\pi}{2}\sin{\frac{\pi (2)}{2}}=0.$
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