Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.1 Maximum and Minimum Values - 3.1 Execises: 41

Answer

The critical numbers are $\pi n$

Work Step by Step

Find the critical numbers of $f(\theta ) = 2\cos \theta + \sin ^2 \theta$ Differentiate and set the derivative $=0$ $f'(\theta) = -2\sin \theta + 2\sin \theta \cos \theta$ $0=2\sin \theta (\cos \theta - 1)$ $f'(\theta) = 0$ when $\sin \theta = 0$ and $\cos \theta = 1$ Therefore, the critical numbers are $\pi n$ and $2\pi n$, which can be simplified down to $\pi n$.
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