How do you find the inflection point of a cubic function?

If $y = f \left(x\right)$ is the cubic, and if you know how to take the derivative $f ' \left(x\right)$, do it again to get $f ' ' \left(x\right)$ and solve $f ' ' \left(x\right) = 0$ for $x$; the inflection point of the curve is at $\left(x , f \left(x\right)\right)$.
The 2nd derivative measures the concavity, down or up, and the inflection point is where that changes from negative to positive, so f" is equal to 0 there.