4. (10 marks] Consider the function f(x,y) = 5x2 + 4xy + y2 -1. (a) Show that f(x, y) has a unique local minimum. (b) Given some initial point xo = (20, yo), compute the gradient vector and Hessian matrix of f(x, y) at xo, and write down the formula of Newton's iteration for minimizing f(x,y). (c) Starting from the initial point xo, how many Newton's iterations does it take to reach the minimizer of f(x, y)? Explain your