I don't feel like I'm understanding the actual concept.
I know that it's concave up when f''(x)>0 but I'm trying to visualise what happens to f(x) when the second derivative becomes positive or negative which I fail to. Sorry for this broad question, but it feels like I don't actually understand it apart from those basic conditions of when it's concave up or down.
Also, To clarify one thing, when the second derivative is zero at a stationary point (ie the x value where the first derivative is equal to zero), this tells us nothing useful right? This is different to when the value of a certain x which makes the second derivative equal zero, right? Because this would tell us the point of inflection?
(Also this is to a final year high school level math extent)