Originally Posted by

**BobP** If it's the case that y = h(x) is a cubic, passes through the origin and the point with

co-ordinates (3,3), and has an inflection at x = 2, (as appears to be from the graph), then you can calculate its equation exactly, (in which case you can then calculate its derivatives exactly). If the co-ordinates of any of those points is in doubt, then you can't.

A good starting point is to assume that $\displaystyle y' =k(x-2)^2=k(x^2-4x+4),$ which gives you an inflection at$\displaystyle x=2.$