JEE Main 2020 (8 Jan, Shift 1) Maths Q58: Let then which…

Question

Let $f(x)=x\cos^{-1}(-\sin|x|)$, $x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$, then which of the following is true ?

Accepted Answer

Option 3: $f'$ is decreasing in $\left(-\frac{\pi}{2},0\right)$ and increasing in $\left(0,\frac{\pi}{2}\right)$

Answer

$f$ is not differentiable at $x=0$

Answer

$f'(0)=-\frac{\pi}{2}$

Answer

$f'$ is decreasing in $\left(-\frac{\pi}{2},0\right)$ and increasing in $\left(0,\frac{\pi}{2}\right)$

Answer

$f'$ is increasing in $\left(-\frac{\pi}{2},0\right)$ and decreasing in $\left(0,\frac{\pi}{2}\right)$

JEE Main 8 January 2020, Shift 1, Maths Q58