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:
- 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 $\frac{\pi}{3}$.
