extreme f(x)=-20x^2-30y^2+560x+360y+180

解答

极值点

f (x) = - 20 x^{2} - 30 y^{2} + 560 x + 360 y + 180

极大值 (14, 6)

求解步骤

找到临界点:

(14, 6)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 60

D (x, y) = 2400

检查在每个临界点处的符号

检查临界点

(14, 6) :

极大值

极大值 (14, 6)

e x t re m e \frac{3 x + 5}{5 x ^{2} + 55 x + 120}

e x t re m e f (x) = x^{4} e^{- 7 x}

e x t re m e f (x) = - 6 x^{\frac{5}{3}} + 3 x

e x t re m e y = 8 + \frac{2}{x}

e x t re m e f (x) = 49 - x^{2}, (- 7, 7)