Choose the correct answer.

f(x) = |log_e |x||, then

Given that the f(x) = |log|x|| where

We can see that function is continuous for all x. Now, checking the points of non differentiability.

LHD at x =1,

RHD at x =1,

∵ LHD ≠RHD

So, function is not differentiable at x =1.

LHD at x =-1,

RHD at x =-1,

∵ LHD ≠RHD

So, function is not differentiable at x =-1.

At x =0 function is not defined.

∴ Function is not differential at x = 0 and ±1.

Hence, option B is correct.