# Find a cubed function knowing the maximum and the point of inflection?

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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What's a "cubed line"? – J. M. Nov 27 '11 at 11:38
And if you mean "cubing function", what do you mean by "maximum"? – David Mitra Nov 27 '11 at 11:50
You have had two requests for clarification, and one answer, and we've not heard anything back from you - are you still there? – Gerry Myerson Dec 1 '11 at 6:35
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. ;-) – amWhy Feb 14 '13 at 14:36

## 1 Answer

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... – J. M. Nov 27 '11 at 12:08