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Question

The function $f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100$ is strictly

decreasing in $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
decreasing in $\left[0, \frac{\pi}{2}\right]$
increasing in $\left(\pi, \frac{3 \pi}{2}\right)$
decreasing in $\left(\frac{\pi}{2}, \pi\right)$

Solution

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