Problem 5: Examine the following function. (2+2+5+6=15 points total) f (x) = f(X,X,)=2x]-3xX2+4x2 X = [X,X, ]I a. Calculate the following partial derivaties at x = [1,2] : of =?, of =? 0x1 x -1, *7-2 Ox2 x1 -1, x3-2 b. Calculate the gradient Vf (x) at x = [1,2]] c. Calculate the directional derivative along vector u = V2 it j using these two methods : 2 2 c-i : D.f(x) = D.f(x) = lim (X+ Au)-f(x) A. c-ii : Daf (x) = Daf(x) = Vf(x) . u d. Calculate the Hessian Matrix H(x) at x = [1,2] X