Monotonicity

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Question

$The length of the longest interval is which the function 3 \sin x - 4 \sin^{3} x is increasing is \frac{π}{k} .$ $Then \frac{k}{2} =$

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Solution

$\begin{array}{l} f (x) = 3 \sin x - 4 \sin^{3} x = \sin 3 x \\ f^{1} (x) > 0 \\ 3 \cos 3 x > 0 \\ 3 x \in (\frac{- π}{2} + \frac{π}{2}) \Rightarrow x \in (- \frac{- π}{6}, \frac{π}{6}) \\ Length = \frac{π}{3} = \frac{π}{k} \end{array}$

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