Let ƒ(x) = xcos–1(–sin|x|), $x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]$, then which of the following is true?

Question

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

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

ƒ '(0) = ${ - {\pi \over 2}}$

ƒ is not differentiable at x = 0

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

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