Originally Posted by

**dannyboycurtis** My question is twofold:

The first one is this:

I need a function which is continuous at only one point and differentiable at only one point.

I claim f(x)={x^2 if x is rational, 0 if x is irrational} is such a function. Is this true?

The second part is, I need a function which is differentiable at only two points and continuous at only one point. This seems impossible to me, unless I am missing something. I have been operating under the assumption that a function must be continuous at a point to be differentiable at that point... any suggestions?