
Re: Some derivative/continuity questions
Posted:
Aug 3, 2013 8:11 PM


On Sat, 3 Aug 2013 13:37:09 0700 (PDT), G Patel <gaya.patel@gmail.com> wrote:
>1) If f is differentiable at x, is it continuous on an interval about x? >It seems intuitively like it should be. > >2) Do you know a function that is differentiable at an isolated point?
Combining ideas from this thread:
f defined by f(x) = 0 for rational x and fx) = 1 for irrational x is not continuous anywhere, but x^2 f(x) is continuous and differentible in only one point.
Leon

