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: 17

Answer

$\pi$/3, $\pi$, and 5$\pi$/3

Work Step by Step

Critical points are points where the derivative of a function is 0 or does not exist. We can take the derivative of h(x) = sin^2(x) + cos(x) by using the chain rule and power rule. Thus, the derivative h'(x) is sin x(2 cos x - 1). By setting the derivative equal to 0, we can find the critical points. sin x = 0 at x = $\pi$ and cos x = 1/2 at x = $\pi$/3 and x = 5$\pi$/3. Thus, the critical points are $\pi$, $\pi$/3 and 5$\pi$/3.
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