a. Show that H2n+1(x) is the unique polynomial of least degree agreeing with f and f at

Chapter 3, Problem 3.3.11

(choose chapter or problem)

a. Show that H2n+1(x) is the unique polynomial of least degree agreeing with f and f at x0,... , xn . [Hint: Assume that P(x) is another such polynomial and consider D = H2n+1 P and D at x0, x1,... , xn .] b. Derive the error term in Theorem 3.9. [Hint: Use the same method as in the Lagrange error derivation, Theorem 3.3, defining g(t) = f (t) H2n+1(t) (t x0)2 (t xn )2 (x x0)2 (x xn )2 [ f (x) H2n+1(x)] and using the fact that g (t) has (2n + 2) distinct zeros in [a, b].]