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受欢迎的函数 >

extreme f(xy)=x^3+y^2-6xy+9x+5y+2

解答

极值点

f (x y) = x^{3} + y^{2} - 6 x y + 9 x + 5 y + 2

解答

极小值 (4, \frac{19}{2}), 鞍点 (2, \frac{7}{2})

求解步骤

找到临界点:

(4, \frac{19}{2}), (2, \frac{7}{2})

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

D (x, y) = 12 x - 36

检查在每个临界点处的符号

检查临界点

(4, \frac{19}{2}) :

极小值

检查临界点

(2, \frac{7}{2}) :

鞍点

极小值 (4, \frac{19}{2}), 鞍点 (2, \frac{7}{2})

作图

流行的例子

extreme f(x,y)=e^{-x-y^2}*(3x-y^2)

e x t re m e f (x, y) = e^{- x - y^{2}} \cdot (3 x - y^{2})

extreme f(x)=((3x-6))/((x+2))

e x t re m e f (x) = \frac{( 3 x - 6 )}{( x + 2 )}

extreme f(x,y)=3x^3-y^3-9x+12y+3

e x t re m e f (x, y) = 3 x^{3} - y^{3} - 9 x + 12 y + 3

extreme f(t)=120-120h(t-2)

e x t re m e f (t) = 120 - 120 h (t - 2)

extreme f(x)=x^6(1-x)^{18}

e x t re m e f (x) = x^{6} (1 - x)^{18}