Consider the following function: 2 f(x₁, x₂) = (2-x₁)² + (2-2x1-x₂) a. (5pt): Obtain the optimum/ optima for this function analytically. Please provide: 1. The optimality conditions used to find the candidate point (s). 2. The candidate point(s) obtained. 3. Arguments supporting whether the point (s) is(are) locally or globally optimal. b. (15pt): Apply a single iteration of the gradient method to find an optimum for this function. Use o = (0,0) as a starting point, a tolerance of = 0.01, and an optimal step size A. You are requested to provide: 1. The expression for the gradient step. 2. The calculations for the optimal step size (analytically). Hint: should be a value close to 0.1). 3. The new point found. 4. Answer the following: is this point optimal? Please justify without relying on the results from (a.). c. (15pt): Apply a single iteration of the Newton's method to find the optimal of this function. Use xo = (0,0) as a starting point, a tolerance of € = 0.01, and an a step size of A = 1. You are requested to provide: 1. The expression for the Newton step. 2. The new point found. 3. Answer the following: is this point optimal? If so, why did the method only took a single iteration? Please justify without relying on the results from (a.). Hint: Remind that if g(x) = (f(x))" then the derivative is g'(x) = nf(x)"-¹ f'(x). Also, [1/2 -1] you need this result for + (c.): [¹04] = [¹/² 5/2). -1 5/2]