Newton's method f(xk) XX+1 = xk f'(x) is a method to find the root r that solves f(r) = 0.

(a) Draw a clearly labeled) picture that shows how Newton's method steps from a current approximation uk to the next approximation 3*+1.

(b) Newton's method is a special case of a fixed point iteration 2k+1 = g(2k). Show that if f'(r) +0, then this fixed point iteration is locally convergent.