If x tends 0 to /2 , then the given function f(x) = x x + x + ^2 … - Vidyadip

MCQ

If $x $ tends $ 0 $ to $\pi /2 $, then the given function $f(x) = x\sin x + \cos x + {\cos ^2}x$ is

A
Increasing
✓
Decreasing
C
Neither increasing nor decreasing
D
None of these

✓

Answer

Correct option: B.

Decreasing

b
(b) $f(x) = x\sin x + \cos x + {\cos ^2}x$

$\therefore f'(x) = \sin x + x\cos x - \sin x - 2\cos x\sin x$

$ = \cos x(x - 2\sin x)$

Hence $x \to 0$ to $\pi $, then $f'(x) < 0$

$i.e.,$ $f(x)$ is decreasing function.

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