If f(x) = x - x 2 is increasing function, then - Vidyadip

MCQ

If $f(x) = \sin x - {x \over 2}$ is increasing function, then

A
$0 < x < {\pi \over 3}$
B
$ - {\pi \over 3} < x < 0$
✓
$ - {\pi \over 3} < x < {\pi \over 3}$
D
$x = {\pi \over 2}$

✓

Answer

Correct option: C.

$ - {\pi \over 3} < x < {\pi \over 3}$

c
(c) $f(x) = \sin x - \frac{x}{2} \Rightarrow f'(x) = \cos x - \frac{1}{2}$

$f'(x) > 0$ for increasing function

Obviously it is increasing for $ - \frac{\pi }{3} < x < \frac{\pi }{3}$.

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