FUNCTION_MANY#extreme f(x,y)=-x^2-y^2+x+2y-1

解答

极值点

f (x, y) = - x^{2} - y^{2} + x + 2 y - 1

极大值 (\frac{1}{2}, 1)

求解步骤

找到临界点:

(\frac{1}{2}, 1)

\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{1}{2}, 1) :

极大值

极大值 (\frac{1}{2}, 1)

e x t re m e g (x) = x^{3} - x^{2} - 8 x - 5

e x t re m e f (x) = \frac{x ^{2} + 1}{x ^{2} - 25}

e x t re m e 2 x^{3} - x^{2} - 4 x + 4

e x t re m e f (x, y) = \frac{2}{x} + \frac{1}{y} + x y

e x t re m e f (x) = 26 x^{2} + 80 x + 64