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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2017 · Mathematics · Application of Derivatives

What is the length of the longest interval in which the function...

What is the length of the longest interval in which the function f(x)=3sin⁡x−4sin⁡3xf(\mathrm{x})=3 \sin \mathrm{x}-4 \sin ^3 \mathrm{x} is increasing?

Options

  1. Aπ3\frac{\pi}{3}
  2. Bπ2\frac{\pi}{2}
  3. C3π2\frac{3 \pi}{2}
  4. Dπ\pi

Correct answer

B. π2\frac{\pi}{2}

Step-by-step solution

f(x)=3sin⁡x−4sin⁡3x=sin⁡3xsin⁡3xf(x)=3 \sin x-4 \sin ^3 x=\sin 3 x\sin 3 x increases in [−π6,π6]\left[\frac{-\pi}{6}, \frac{\pi}{6}\right] So, interval length =π3\frac{\pi}{3}
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