Consider the fixed point iteration xk+1 = g(xk), k = 0, and let all the assumptions of the fixed point theorem hold. use a taylor’s series expansion to show that the order of convergence depends on how many of the derivatives of g vanish at x = x∗. use your result to state how fast (at least) a fixed point iteration is expected to converge if g′(x∗) = ··· = g(r)(x∗) = 0, where the integer r ≥ 1 is given.