Consider the fixed point iteration x(sub k+1) = g(x(sub k)), k=0,1,..., 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 interger r>=1 is given.