JEE Main 20208 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002Let ƒ(x) = xcos^–1(–sin|x|), x∈[−π2,π2]x \in \left[ { - {\pi \over 2},{\pi \over 2}} \right]x∈[−2π,2π], then which of the following is true?AOption A. ƒ' is decreasing in (−π2,0)\left( { - {\pi \over 2},0} \right)(−2π,0) and increasing in (0,π2)\left( {0,{\pi \over 2}} \right)(0,2π)BOption B. ƒ '(0) = −π2{ - {\pi \over 2}}−2πCOption C. ƒ is not differentiable at x = 0DOption D. ƒ' is increasing in (−π2,0)\left( { - {\pi \over 2},0} \right)(−2π,0) and decreasing in (0,π2)\left( {0,{\pi \over 2}} \right)(0,2π)CheckSkip · show solution
