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受欢迎的函数 >

extreme f(x)=5x^2y-3xy^2-4x+3y

解答

极值点

f (x) = 5 x^{2} y - 3 x y^{2} - 4 x + 3 y

解答

鞍点 \frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3}, 鞍点 - \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3}

求解步骤

找到临界点:

\frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3}, - \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3}

\frac{\partial ^{2} f}{\partial x ^{2}} = - 6 x

D (x, y) = - 100 x^{2} + 60 x y - 36 y^{2}

检查在每个临界点处的符号

检查临界点

\frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3} :

鞍点

检查临界点

- \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3} :

鞍点

鞍点 \frac{9 + 21}{5 2 3 + 21}, \frac{2 ( 3 + 21 )}{3}, 鞍点 - \frac{9 + 21}{5 2 3 + 21}, - \frac{2 ( 3 + 21 )}{3}

作图

流行的例子

extreme f(x)=tan(x)[-5,6]

e x t re m e f (x) = tan (x) [- 5, 6]

extreme-x^3+x^2+x+8

e x t re m e - x^{3} + x^{2} + x + 8

extreme x^3+y^2+12xy+1

e x t re m e x^{3} + y^{2} + 12 x y + 1

extreme-(40/3)/(x^2)+0.54x

e x t re m e - \frac{\frac{40}{3}}{x ^{2}} + 0.54 x

extreme f(x,y)=x*e^y

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