question_answer

Let 5 be the set of all points in \[(-\pi ,\pi )\]at which the function, \[f(x)=\min \{\sin x,\cos x\}\]is not differentiable. Then S is a subset of which of the following? [JEE Main Online Paper Held On 12-Jan-2019 Morning]

A) \[\left\{ -\frac{\pi }{4},0,\frac{\pi }{4} \right\}\]                            

B) \[\left\{ -\frac{3\pi }{4},-\frac{\pi }{4},\frac{3\pi }{4},\frac{\pi }{4} \right\}\]

C) \[\left\{ -\frac{3\pi }{4},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{4} \right\}\]

D)               \[\left\{ -\frac{\pi }{2},-\frac{\pi }{4},\frac{\pi }{4},\frac{\pi }{2} \right\}\]

Correct Answer: B

Solution :

Here, \[y=\min [\sin x,\cos \,x]\]is not differentiable at \[\left\{ -\frac{3\pi }{4},\frac{\pi }{4} \right\}.\]