Problem 9: Show that the function at) = 8m + 12$2 + :13? 232% has only one stationary point, and that it is neither a maximum nor minimum, but a saddle point. Problem 10: Consider the function f($1,:r2) = ($1 + 3:3]2 At the point xT = (1, 0] consider the search direction HIT = (1.1). Show that d is a descent direction and nd all minimisers of the problem ' ('6) [gig f(:r + Adk) Problem 11: 11.1 Consider a convex quadratic objective function f of the form: f(:r) = mTAr: + bTrr + c with a symmetric positive definite matrix A, r 6 IR" and a vector b E R". Assuming the steepest descent with an 'exact line search' approach is used to approximate the minimiser. Show that the step-length at k-th iterate takes the form: Where 9;; = Vf(:r{f)). 11.2 Consider the function f(:t1,m2] = 1r+ 331332 + 2mg. Compute the first two iterates mil) and {17(2) of the steepest descent method using exact line search applied to the objective function f(:rl, :52) starting with 3(0) 2 (2, ~2). 11.3 Find the minimum of the function 2 1 2 +32 MIO'I f($1,.'2) = $33 using the conjugate gradient method (algorithm attached in Appendix) starting \"an. mm) _ m 1