Recently I have started studying (1-dimensional) dynamical systems and the first thing that I came across fixed points, specifically hyperbolic and non-hyperbolic fixed points.
What would be an example of a $C^2$ map $f: \mathbb{R} \rightarrow \mathbb{R} \;$that has a non-hyperbolic fixed point $x_0$, i.e. $f'(x_0)=1$, where $x_0$ can be stable or unstable.
Part where $x_0$ can be stable or unstable, but not exponentially stable is where I get confused, which is why I was looking for an example to help me illustrate that.