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

a. Show that H_2n+1(x) is the unique polynomial of least degree agreeing with f and f ' at x₀, . . . , x_n. [Hint: Assume that P(x) is another such polynomial and consider D = H_2n+1 − P and D ' at x₀, x₁, . . . , x_n.]

b. Derive the error term in Theorem 3.9. [Hint: Use the same method as in the Lagrange error derivation, Theorem 3.3, defining

Reference: Theorem 3.9

Reference: Theorem 3.3