Interpolation- Lagrange polynomial

Question

Let $x_0,x_1,...,x_n$ will be different real numbers. Show, that: $f[x_0,x_1,...,x_n]=\sum_{i=0}^m\frac{f(x_i)}{\Phi '(x)}$ where $\Phi (x)=(x-x_0)(x-x_1)...(x-x_m)$ So, I have some problems.How to start?

Answer 1

I guess $f$ is defined as the minimum polynomial with $f(x_i)=y_i$. You get two polynomials of same order $n$, equal on $n+1$ points. They are equal.