First of all sorry if my question could be too trivial for the standards of this site but I am not so expert.
I am studying how perform the qualitative plots of functions of real variables. In particular I am interested in understand the relation in between the first derivative and the second derivative.
I mean: if I have a function that is always increasing, more specifically always strictly increasing, i.e $f'(x)>0$ $\forall x\in \mathbb{R}$, then is it possibile that there exists a point in which the function passes from a phase of "acceleration" to a phase of "deceleration", so from convexity to concavity?
$\textbf{So the question is:}$ is it possible that a function always strictly increasing has a flex point (where the second derivative is null)? I am trying to think about some examples but I can't...maybe my fault since I'm just getting started in studying all these stuffs.
EDIT: I have thought $x^3$ that is strictly increasing but has a flex point in $0$, am I right?