I only need help on problem 2, but I have attached problem 1 just in case you need it.

Problem 1: Suppose you are given A E Rx symmetric positive definite, bE R", and c E R, and you are considering the function f : R" -> R defined by f(x) = 2x Ax+b x+c. Now, suppose you are given a particular point a E R" and a nonzero direction d E R". Derive the optimal solution to the one-dimensional subproblem min f (x + ad) such that a E R. Hint: The answer will be that the optimal value a is a* = _ (Axtb)'d dT Ad Problem 2: Suppose you want to minimize the function f : R2 - R given by, for all x E R2, f (x) = >a Ax + blx +c where A = [18 1], b = , and c = 10. a) Solve this optimization problem exactly using first and second order conditions. b) Show that for any initial guess x, steepest descent method generates a (1), x (2), x(3), x(4) ..., where, for all k, x(k+1) = x*) + Ad d' d d with d = -(Ax() + b). Hint: Use Problem 1