Hey, I am struggling with coming up with an example of a function that is differentiable on the integers but non-differentiable everywhere else. I have tried looking at various piecewise functions, but none seem to work. I was thinking
f(x)= 0 if x is an integer
f(x)= 1/q if x is rational
and then i don't know what to do if f(x) is irrational.
I know that I am looking for a function that will be discontinuous and therefore nondifferentiable on at non-integer values.
Since I want it to be differentiable on the integers, I want my function to be continuous at the integers.
I know these things, but I cannot seem to connect the dots and it's driving me insane. Please help!
I'm still confused at your example. I think I understand what you're trying to do, but I'm not seeing how the function is differentiable at every integer and not differentiable anywhere else. Is there an easier example that would be less difficult to comprehend?