Write the points of non-differentiability of f(x) = |log|x||.

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

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.