✔ 最佳答案
f_x(x,y) = 3x^2-3,
f_y(x,y) = 3y^2 - 6y
解 f_x(x,y)=0, f_y(x,y)=0 得 x=±1, y=0 or 2.
f_xx(x,y) = 6x
f_yy(x,y) = 6y-6
f_xy(x,y)=0=f_yx(x,y)
將 stationary points (x,y) = (-1,0), (1,0), (-1,2), (1,2)
一一代入, f_xx(x,y) 與 f_yy(x,y) 正負相反者即是鞍點所在.
結果得 (1,0), (-1,2) 有鞍點.
f(1,0) = 2, f(-1,2) = 2.,
故鞍點為 (1,0,2) 與 (-1,2,2).
以上如有計算錯請自行更正.