extreme f(x,y)=x^2+y^2+(16)/x+2/y

解答

极值点

f (x, y) = x^{2} + y^{2} + \frac{16}{x} + \frac{2}{y}

极小值 (2, 1)

求解步骤

找到临界点:

(2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 + \frac{4}{y ^{3}}

D (x, y) = (\frac{4}{y ^{3}} + 2) (\frac{32}{x ^{3}} + 2)

检查在每个临界点处的符号

检查临界点

(2, 1) :

极小值

极小值 (2, 1)

e x t re m e f (x) = - 5 x^{4} - 5 x^{3} - 2

e x t re m e f (x) = - x^{3} - 6 x^{2} - 1

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

e x t re m e y = - 4 x^{2} - 5 x + 1

e x t re m e f (x) = \frac{x ^{2} - 7 x - 6}{x - 5}