extreme F(X,Y)=3X+2X^2+4Y+Y^2-2XY

解答

极值点

F (X, Y) = 3 X + 2 X^{2} + 4 Y + Y^{2} - 2 X Y

极小值 (- \frac{7}{2}, - \frac{11}{2})

求解步骤

找到临界点:

(- \frac{7}{2}, - \frac{11}{2})

\frac{\partial ^{2} f}{\partial X ^{2}} = 2

D (X, Y) = 4

检查在每个临界点处的符号

检查临界点

(- \frac{7}{2}, - \frac{11}{2}) :

极小值

极小值 (- \frac{7}{2}, - \frac{11}{2})

e x t re m e f (x) = 8 x^{2} - 6 x^{4}

e x t re m e T (x, y) = 27 - 8 x^{2} - 9 y^{2}

e x t re m e f (x, y) = x^{3} + y^{2} + x y + y

e x t re m e f (x) = x^{5} - 5 x + 6

e x t re m e f (x) = 2 x^{2} + 3 x y + 4 y^{2} + 2 x - 10 y