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

Show that the cubic Hermite polynomial H3(x) can also be written as f [z0] + f [z0, z1](x ˆ’ x0) + f [z0, z1, z2](x ˆ’ x0)2 + f [z0, z1, z2, z3](x ˆ’ x0)2(x ˆ’ x1).

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