Question Number 101510 by bemath last updated on 03/Jul/20

What are all critical point  for f(x,y) = 2x^2 −y^3 −2xy

Commented bybramlex last updated on 03/Jul/20

(1)(∂f/∂x) = 4x−2y=0 , y = 2x  (2) (∂f/∂y) = −3y^2 −2x= 0 , 2x=−3y^2   (3) ⇒2y = 2(−3y^2 ) ; 3y^2 +y = 0  y(3y+1)=0 → { ((y_1 =0 ∧x_1 = 0)),((y_2  = −(1/3) ∧x_2  = −(1/6))) :}  so critical point are (0,0) & (−(1/6), −(1/3)) ▲