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MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If f(x)=min⁡{1,cos⁡x,1−sin⁡x}f(x)=\min\{1,\cos x,1-\sin x\} for −π≤x≤π-\pi\le x\le\pi, then (1) f(x)f(x) is differentiable at 00. (2) f(x)f(x) is differentiable at π2\frac{\pi}{2}. (3) f(x)f(x) has a local maximum at 00. (4) None of the above.

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