The length of the longest interval, in which the function 3 x - 4… - Vidyadip

MCQ

The length of the longest interval, in which the function $3\sin x - 4{\sin ^3}x $ is increasing, is

✓
${\pi \over 3}$
B
${\pi \over 2}$
C
${{3\pi } \over 2}$
D
$\pi $

✓

Answer

Correct option: A.

${\pi \over 3}$

a
(a) $3\sin x - 4{\sin ^3}x = \sin 3x$

It is increasing, when $ - \pi /2 \le 3x \le \pi /2$

$i.e.,$ $ - \pi /6 \le x \le \pi /6$.

$\therefore$ The length of interval $= \left| {\,\frac{\pi }{6} - \left( { - \frac{\pi }{6}} \right)\,} \right|\, = \,\frac{\pi }{3}$.

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