Q232 / 270 · NDA 2017 (Phase 1) · Mathematics

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

  • A
    $\frac{\pi}{3}$
  • Correct answer
    B
    $\frac{\pi}{2}$
  • C
    $\frac{3 \pi}{2}$
  • D
    $\pi$

Solution

$f(x)=3 \sin x-4 \sin ^3 x=\sin 3 x$ $\sin 3 x$ increases in $\left[\frac{-\pi}{6}, \frac{\pi}{6}\right]$ So, interval length $=\frac{\pi}{3}$

Hence, the correct answer is option: 'B'.

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