# Do derivatives always exist in a neighborhood?

1. Sep 21, 2010

### slamminsammya

Suppose that $$f:\mathbb{R} \to \mathbb{R}$$ is continuous and $$f'(x_0)$$ exists for some $$x_0$$ . Does it follow that $$f'$$ exists for all $$x$$ such that $$|x-x_0|<r$$ for some $$r>0$$ ?

2. Sep 21, 2010