5. (20 pts) Find the global maximum value of f(x, y) = 100 -x2 - and find the point (x, y) where it has a global maximum. Birefly explain your answer. You can use your own argument or the second derivative test. (0 10) = point of maximum f (x , y ) = 100 - x 2 - yz value S= - 2X Global max value = 100 -2X = 0 OO SV = - 2y t - zy = -2X = 0 - 24 = 0 Sxx = - 2 - 2 = - 2 - 2 - 2 Syy = - 2 X = 0 Y=0 Sxy = 0 The local maximum is at D = - 20- 2- (0)2 ( 0. 0). since D is positive and D = +4 the partial second derivative with respect to x is negative, that means that the critical point ( 0,0 ) is a maximum local Explany, why lobil max. ' CT