Let $f: \Bbb R \to \Bbb R$ be a derivable function. $f'$ is uniformly continuous in $\Bbb R$
Prove that $[n(f(x+1/n)-f(x))]$ converges uniformly to $f'(x)$
I'm having a hard time seeing why does $f'$ being uniformly continuous help me and I tried to assume negatively that it doesn't converge uniformly but that didn't really get me anywhere.
edit: Can anyone think of a derivable function that its derivative isn't uniformly continuous and doesn't maintain:$[n(f(x+1/n)−f(x))]$ converges uniformly to $f'(x)$ ?