Let z0 = x0, z1 = x0, z2 = x1, and z3 = x1. Form the following divided-difference table

Chapter 3, Problem 3.3.12

(choose chapter or problem)

Let z0 = x0, z1 = x0, z2 = x1, and z3 = x1. Form the following divided-difference table. z0 = x0 f [z0] = f (x0) f [z0,z1] = f (x0) z1 = x0 f [z1] = f (x0) f [z0,z1,z2] f [z1,z2] f [z0,z1,z2,z3] z2 = x1 f [z2] = f (x1) f [z1,z2,z3] f [z2,z3] = f (x1) z3 = x1 f [z3] = f (x1) Show that the cubic Hermite polynomial H3(x) can also be written as f [z0] + f [z0,z1](x x0) + f [z0,z1,z2](x x0) 2 + f [z0,z1,z2,z3](x x0) 2 (x x1).