임계점:
f_x = 3x^2 - 3y = 0 \;\Rightarrow\; y = x^2.
f_y = 3y^2 - 3x = 0 \;\Rightarrow\; x = y^2.
(x^2)^2 = x^4. \;\Rightarrow\;x^4 - x = 0 \;\Rightarrow\; x(x^3 - 1)=0 \;\Rightarrow\; y=0,\; x=1.
\;\Rightarrow\; y=1. 임계점: (0,0),\ (1,1).
2차 도함수: f_{xx} = 6x,\quad f_{yy} = 6y,\quad f_{xy} = -3.
판별식 D: D(x,y)=f_{xx} f_{yy} - (f_{xy})^2 = 36xy - 9.
• (0,0): (D(0,0)=0 - 9 = -9 < 0. 안장점
• (1,1): (D(1,1)=36 - 9 = 27 > 0,\quad f_{xx}(1,1)=6>0. 극솟값