For an interval [a,b], define h = (b-a)/n , n>0. Define evenly spaced node points by:
x(sub)j = a + jh, j=0,1,...,n
Thus, x(sub)0 = a, x(sub)1 = a + h + ... and x(sub)n = a + nh = b.
consider the polynomail f(sub)n = (x - x0)(x - x1) ... (x - xn)
and show:
|f(sub)n| <= n!h^(n+1), a<=x<=b
Any advice...