What are all the critical points of the function f(x, y) = -3 . y . 2 + y . 2 - 2 . y. 2. Enter your answer as a set of vectors (each with square brackets): {[a, b] , [c, d] , .. .} for appropriate numbers a, b, c, d, ... Battery status: 41% Check (3) standard function logic vector abc unit Search Th ENG . US 17 FO FIC F Pri So Insert Delete 8 O Backspaceand of ay - - 3 x +ayn - an = o - M ( - 3 x+ 2 4 - 2 ) = 0 n= 0 or - 3xtay-2=0 = ] - 3ntay-2=0 -(i) Put 1= O into ( 1) . we get, J - 610)-2=0 y = 2 Put 4=0 into cill we get , - 31+2 (0) - 2 = 0 J - 3x- 2 = 0 n = =(3) Put (i) equal to cil) . we get. J- 6n- 2 = - 3xtay- 2 7 4- Q4 =61-3x1 y = 3x y = - 3x() Put it into (i) . we get, - 31-61- 2=0 1 - 91- 220 MS - Put it into (! !) . we get, y = - 3 ( 2 ) = 3 Hence, critical points are given by [ogo], 10, 2], (- 290], [- 293Let fly. y ) = - 3 4x2 + 4x- ayn To find critical points of the function. Take partial derivative of f (x,y) with respect tone. We get, at = - Gyn + y ?_ ay an Now, partial derivative of f (1,y ) with respect to y . we get, of = - 3x2 + 2yn- 2n ay For critical points, of -=0 at 20 an ay Consider, of = 0 =- 6 yx + yz ay= 0 an - y ( - 6 + y - 2 ) = 0 - y=o or y- 671- 2 = 0 - (1 )