question_answer

The function \[y\,=\,|\sin x|\] is continuous for any x but it is not differentiable at [AMU 2000]

A)            \[x=0\] only                               

B)            \[x=\pi \] only

C)            \[x=k\,\pi \,(k\] is an integer) only

D)            \[x=0\] and \[x=k\,\pi \,(k\] is an integer)

Correct Answer: D

Solution :

           It can be easily seen from the graph of \[f(x)=\,|\sin x|\] that it is every where continuous but not differentiable at integer multiples of \[\pi \] and at \[x=0\].