# 9. Prove that the function f given by  is not differentiable at x = 1.

Given function is

We know that any function is differentiable when both
and         are finite and equal
Required condition for function to be differential at x  = 1 is

Now, Left-hand limit of a function at x = 1 is

Right-hand limit of a function at x = 1 is

Now, it is clear that
R.H.L. at x= 1    L.H.L. at x= 1
Therefore, function  is not differentiable at x = 1

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