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

解答

极值点

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

极小值 (0, 1)

求解步骤

找到临界点:

(0, 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

(0, 1) :

极小值

极小值 (0, 1)

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

e x t re m e f (x, y) = - [x^{2} - y^{2}] e^{- x^{2} - y^{2}}

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

e x t re m e f (x) = 6 x^{5} - 2 x^{4}

e x t re m e f (x) = - x^{3} + 3 x^{2} + 2880 x - 500