Application of Derivatives 2 Question 9

####9. The length of a longest interval in which the function $3 \sin x-4 \sin ^{3} x$ is increasing, is

(2002, 2M)

(a) $\frac{\pi}{3}$

(b) $\frac{\pi}{2}$

(c) $\frac{3 \pi}{2}$

(d) $\pi$

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Answer:

(a)

Solution:

  1. Let $f(x)=3 \sin x-4 \sin ^{3} x=\sin 3 x$

The longest interval in which $\sin x$ is increasing is of length $\pi$.

So, the length of largest interval in which $f(x)=\sin 3 x$ is increasing is $\frac{\pi}{3}$.



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