Let Xo < X1 < ....... < Xn and let f(x) be continuously differentiable. Show that:
d/dxi f[Xo.......Xn] = f[Xo.......Xi,Xi+1......Xn]
I have absolutely no idea how to go about this one. Can I get some hints pleasE?
ok, so the only relevant divided difference theorem is
TheoremLet 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?