# Determining polynomial coefficients by known derivatives

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### Accepted Answer

Dr. Seis
on 18 Oct 2012

Edited: Dr. Seis
on 18 Oct 2012

Yes. Just in case this is homework, I will give an example to get you started.

Let's say you have the case below (I will start with the case where we do not have derivatives at a location).

We are trying to solve for A, B, and C

y(x) = A*x^2 + B*x + C

Knowns:

x1 = 0; y1 = 1;

x2 = 3; y2 = 6;

x3 = 7; y3 = 7;

So we can construct an inverse problem of the form G * m = d, where:

G = [x1^2,x1,1; x2^2,x2,1; x3^2,x3,1];

d = [y1; y2; y3];

We determine m (equal to [A; B; C] in our example) by:

m = G\d;

And we get:

plot(-1:10,polyval(m,-1:10),'r-', [x1,x2,x3],[y1,y2,y3],'k+')

### More Answers (1)

Suzie Oman
on 8 Jul 2017

This answer doesn't incorporate the derivative. How would this be solved taking into account the derivative?

What about in 3 dimensions?

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