# Thread: Newton Divided Difference Problem

1. ## Newton Divided Difference Problem

So my problem says:
Given the below data of polynomial P(x), determine the coefficient of all x2 in P(x) if all third-order Newton divided difference are 1

x 0 1 2

P(x) 2 -1 4

What I did was find the First and second order divided differences. I think I might have done the problem incorrectly though, because I didn't use that the third order difference is 1. I was taught that the coefficient of x2 would be the second order divided difference, so I just found that using the data points.

I got: f[x0,x1]=-3, f[x1,x2]=5, and f[x0,x1, x2]=-4
I thought 4 would be the coefficient, but the back of the book says its 3.5. Any help?

2. ## Re: Newton Divided Difference Problem

Since the third order difference is constant, we know that we must have:

$P(x)=Ax^3+Bx^2+Cx+D$

Since the third order difference is 1, we have:

$P'''(x)=6A=1\:\therefore\:A=\frac{1}{6}$

Now, we are given:

$P(0)=D=2$ and this results in the 2X2 system:

$B+C=-\frac{19}{6}$

$4B+2C=\frac{2}{3}$

Solving this system, we find:

$B=\frac{7}{2}$

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# determine the coefficient of x3 if all the 4th order forward differenced are 1

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