Given a function f and an unique interpolation polynomial P, we can say that for every x there is a r so that
$f(x)-P(x)=\frac{\omega(x)f^{n+1}(r)}{(n+1)!}$
where r is in the smallest interval $[x_0,...x_n,x]$ that contains x and all support points of P.
Now I need to show that for $h:=max_{i=0,n-1} (x_{i+1}-x_{i})$
we can estimate $\omega$ as
$max_{x\in[x_0,x_n]}|\omega(x)| \leq \frac{n!}{4}h^{n+1})$
We know that $\omega =(x-x_0)(x-x_1)...(x-x_n)$.
I tried to transform the very first formula because the estimation contains a factorial but unfortunately I don't really see how I can show this estimation.