Corollary 1. 2(Newton Approximation). Assume that PN(a)is the New- ton polynomial given in Theorem 1.5 and is used to approximate the function f(r), that is, f(a)=PN()+en(a) If fE CN+a, bl, then for each a E a, b there corresponds a number=c( in(a, b), so that the error term has the form EN(a) (x-x0)(x-2x1)…(x-xrx)f(N+(c) (N+1)