1. ## Divided Differences

Let Xo < X1 < ....... < Xn and let f(x) be continuously differentiable. Show that:

d/dxi f[Xo.......Xn] = f[Xo.......Xi,Xi+1......Xn]

2. ok, so the only relevant divided difference theorem is

Theorem
Let f be n times continuously differentiable on [a; b], and let x0; x1; : : : ; xn be distinct
points in
[a; b]. Then there exists a number eta in[a; b] such that

f
[x0; x1; : : : ; xn] = f(n)(eta)/n!

any hints?