Differentiability at a point

For

I want to know where is differentiable/not differentiable. I know it is differentiable at .. but I kind of cheated and used the Squeeze Theorem to prove that.

I now want to that to show that is *not* differentiable at the only other point where it is continuous, i.e. at . I don't know how to show it explicitly in limit form, however.

Any help or tips are appreciated - thanks in advance!

Re: Differentiability at a point

The limit form requires that for any there is a , such that if .

However, if , there is always an h, for which this is not true (for any and any choice of f'(x)).

This is the case, since between any 2 different rational numbers, there is always an irrational number.

And between any 2 different irrational numbers, there is always a rational number.

Re: Differentiability at a point

Worded very well - thanks so much. I didn't think about using that form of limit.