The length of the longest interval in which the function $3 sin x - 4 {sin}^{3} x$ is increasing is

\frac{π}{3}

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\frac{π}{2}

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\frac{3 π}{2}

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π

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Solution

The correct option is A $\frac{π}{3}$
$3 sin x - {sin}^{3} x = sin 3 x$
Since $sin x$ increases in $[- \frac{π}{2}, \frac{π}{2}]$
Therefore $sin 3 x$ increases in $[- \frac{π}{6}, \frac{π}{6}]$
Therefore length of the interval= $\frac{π}{3}$
Ans: A

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