Newton's interpolating polynomial

[fluidistic]

Homework Statement

Interpolate the function ln(x+1) using a Newton's polynomial of degree 2. The points to be interpolated are $x_0=0$, $x_1=0.6$ and $x_2=0.9$.

Homework Equations

$p_2(x)=c_0+c_1(x-x_0)+c_2(x-x_0)(x-x_1)$.

The Attempt at a Solution

So I used divided differences in order to calculate the coefficients of the polynomial.
$f[x_1, x_2]=\frac{f(x_2)-f(x_1)}{x_2-x_1} \approx 0.1718502569$.
$f[x_0,x_1]\approx 0.7833393821$.
$f[x_0,x_1,x_2]=\approx -0.6794$.
This gives $c_0=0, c_1\approx 0.78$ and $c_2 \approx -0.68$.
I've plotted both ln(x+1) and the polynomial and... it doesn't fit as it should. In fact it interpolates ln(x+1) in 0 and 0.6 but not in 0.9 as it should.
Where did I go wrong?! I've redone the algebra twice, even with a calculator and I'm still getting this wrong result.
Thanks for any help.

 

[TheoMcCloskey]

fludistic - I get a different value for c2 of approx -.2344... Don't forget, your data is spaced unequally.

 

[fluidistic]

fludistic - I get a different value for c2 of approx -.2344... Don't forget, your data is spaced unequally.

Thanks. I've redone all from scratch and now get your result. :)