JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

Let

f(x)=x \cos ^{-1}\left(\sin (-|x|), x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\right.

Then,

View answer and explanation

Correct option: D

f^{\prime}(x)

is decreasing in

\left(-\frac{\pi}{2}, 0\right)

and increasing in

\left(0, \frac{\pi}{2}\right)

Option D (

f^{\prime}(x)

is decreasing in

\left(-\frac{\pi}{2}, 0\right)

and increasing in

\left(0, \frac{\pi}{2}\right)

) is correct because the second derivative is negative for negative x and positive for positive x.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

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f

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\left( { - \infty ,\;\infty } \right)