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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!

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    graphtheory92: remember to upvote, and/or accept answers you find to be helpful. You can accept one answer per question, but you can upvote any/all answers that are correct, that help, etc. ;-)2013-02-14

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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.

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    This is in fact a Hermite interpolation problem...2011-11-27