Assertion : The length of a longest interval in which the function $f (x) = 3 \sin x - 4 \sin^{3} x$ is increasing is $\frac{π}{2}$
Reason : The function $f (x)$ is increasing if $f^{1} (x) \leq 0$

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Both Assertion and Reason are true and Reason is the correct explanation of the Assertion.

Both Assertion and Reason are true and Reason is not the correct explanation of the Assertion

Assertion is true ,but Reason is false

Assertion and Reason both are false

answer is D.

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Detailed Solution

$f (x) = \sin 3 x f^{1} (x) = 3 \cos 3 x$

$f^{1} (x) = 0 \Rightarrow 3 \cos 3 x = 0 \Rightarrow 3 x = (2 n + 1) \frac{π}{2} \Rightarrow x = (2 n + 1) \frac{π}{6} \Rightarrow x = \frac{π}{6}, \frac{3 π}{6}, \frac{5 π}{6} L e n g t h = \frac{5 π}{6} - \frac{3 π}{6} = \frac{2 π}{6} = \frac{π}{3}$