extreme F(x,y)=x^2+xy+y^2+3x-3y+4

解答

极值点

F (x, y) = x^{2} + x y + y^{2} + 3 x - 3 y + 4

极小值 (- 3, 3)

求解步骤

找到临界点:

(- 3, 3)

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

D (x, y) = 3

检查在每个临界点处的符号

检查临界点

(- 3, 3) :

极小值

极小值 (- 3, 3)

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

e x t re m e f (x) = (4 x - 1)^{2}

e x t re m e f (x) = 5 x^{2} - 10 x + 2, - 4 \leq x \leq 2

e x t re m e f (x) = x + sin (x), - \frac{π}{2} \leq x \leq \frac{π}{2}

e x t re m e f (x, y) = 8 x^{2} + 7 y^{2}