Is it possible to find the function of a cubed line if we know its maximum and its point of inflection?
if yes, can some one explain me?
Thank you very much!
Is it possible to find the function of a cubed line if we know its maximum and its point of inflection?
if yes, can some one explain me?
Thank you very much!
I'm going to assume that there's an equation $y=ax^3+bx^2+cx+d$ where $a,b,c,d$ are unknowns to be found - if that's not what you have in mind, please clarify.
I also assume you know there is a local maximum at $(r,s)$, and a point of inflection at $(u,v)$.
So what you know is $y(r)=s$, y'(r)=0, $y(u)=v$, and y''(u)=0. Well, that's four linear equations in four unknowns, I'm sure you can handle that.
EDIT: As J.M. notes in the comments, this is an example of Hermite interpolation.