A function f is defined by:
where and [.] denotes the greatest integer function.
Discuss the continuity and differentiability of at
It follows that is not diffrentiable at , because it is not continuous.
At , we have: .
Looking at and assuming (I think this is OK to assume because we want ), we know that and , so as becomes less than , we have:
Looking at and assuming , we know that , and we have:
So I think is differentiable at , and furthermore that and the tangent line is .
I'm only moderately confident about this response.