Numerical analysis

2. (a) By equating the leading coefficient of the Lagrange form of the interpolating polynomial Pn (x) with that of Newton's form, deduce that n f [xo, X1, ..., In] f (x; ) = j=0 ITk=0,kaj (20; - k) (b) Use part (a) to conclude that any permutation of To, 1, ..., In leaves the cor- responding divided difference unchanged