Application Of Derivatives Ques 57
57. 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) $\pi$
Show Answer
Answer:
(a)
Solution:
Formula:
Increasing and decreasing of a function:
- 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 $\frac{\pi}{2}$.
So, the length of the largest interval in which $f(x)=\sin 3 x$ is increasing is $\frac{\pi}{3}$.
BETA
