general equation to find cubic polynomial from two minimums? I tried researching and found that I can use a system of linear equations and solve by an inverse matrix to find the cubic equation given 4 points which satisfy the function f(x) of the general form $f(x)=ax^3+bx^2+cx+d$
I can also find a cubic of the form $ax^3 + d$ with no $x^2$ or $x$ term from 2 points, however I was wondering how one would go about finding a full general form cubic given only the minimum and maximum. 
Example minimums could be (-1,4) and (2,3)

Well, since the extrema are the roots of the derivate, it would be nice to have the minimum and the maximum (and an initial condition too.)
