Question : How would one prove the following theorem ? If anyone knows the name of it or where I can look it up, please provide a link or a proof.
Theorem (Asymptotically unstable stability) : Consider the dynamical system $x'=f(x)$, where $f: D \to \mathbb R$ a continuously differentiable function at the open interval $D \subset \mathbb R$ with $f(0) = 0$. Show that the point $0\in D$ is asymptotically unstable, if $|f'(0)|<1$.