A sequence $(f_n)$ of differentiable functions such that both $(f_n)$ and $(f'_n)$ converge uniformly but $f = \lim f_n$ is not differentiable at some point.
Thoughts so far:
We are taking the domain of these functions as all of $\mathbb{R}$.
I am under the impression that this request might be impossible since we can simply apply the Differentiable Limit Theorem. Is this correct or am I missing something?
