Applications Of Derivatives Question 273
Question: The length of the longest interval, in which the function $ 3\sin x-4\sin x $ is increasing, is
[IIT Screening 2002]
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{2} $
C) $ \frac{3\pi }{2} $
D) $ \pi $
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Answer:
Correct Answer: A
Solution:
$ 3\sin x-4{{\sin }^{3}}x=\sin 3x $ It is increasing, when $ -\pi /2\le 3x\le \pi /2 $ i.e., $ -\pi /6\le x\le \pi /6 $ . The length of interval = $ | ,\frac{\pi }{6}-( -\frac{\pi }{6} ), |,=,\frac{\pi }{3} $ .
BETA
