Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 4 - Applications of the Derivative - 4.4 The Shape of a Graph - Exercises - Page 194: 7


Concave upwards for all $\theta$ in (0,$\pi$) and concave down for all $\theta$ in ($\pi, 2\pi$). The point of inflection is at $\theta=\pi$.

Work Step by Step

$y=f(\theta)=\theta-2\sin \theta$ $f'(\theta)=1-2\cos\theta$ $f''(\theta)=-2\times-\sin\theta=2\sin\theta$ $f''(\theta)$ is positive when $\theta\in(0,\pi)$ and is negative when $\theta\in (\pi,2\pi)$.
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