extreme f(x)=x^2+xy+y^2-4y+5

解答

极值点

f (x) = x^{2} + x y + y^{2} - 4 y + 5

极小值 (- \frac{4}{3}, \frac{8}{3})

求解步骤

找到临界点:

(- \frac{4}{3}, \frac{8}{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

(- \frac{4}{3}, \frac{8}{3}) :

极小值

极小值 (- \frac{4}{3}, \frac{8}{3})

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

e x t re m e f (x) = 2 x^{2} ln (x) - 21 x^{2}

e x t re m e \frac{x + 1}{x ^{2} - 8 x - 9}

e x t re m e f (x) = 2 x^{3} - 9 x^{2} - 24 x + 20

e x t re m e f (x) = 3 x^{2} + y^{2} - 6 x - 4 y + 7