Explain why the secant formula XXXXXXXXXXwould be preferred to the following equivalent expression:                              xn+1 = [xn−1g(xn) − xng(xn−1)]/[g(xn) − g(xn−1)]. Suppose we are given...

Explain why the secant formula (8.3.7) would be preferred to the following equivalent expression:

                             xn+1 = [xn−1g(xn) − xng(xn−1)]/[g(xn) − g(xn−1)].

Suppose we are given f ∗ (0), f ∗ (1), and f ∗(0). Following Exercises 8.18 and 8.3, find the value of u that minimizes a quadratic approximation to f ∗ (u).