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受欢迎的函数 >

extreme f(x)=x^2e^{1-x}

解答

极值点

f (x) = x^{2} e^{1 - x}

解答

极小值 (0, 0), 极大值 (2, \frac{4}{e})

求解步骤

f^{'} (x) = e^{1 - x} x (2 - x)

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < 2,

递减

: 2 < x < \infty

将

x = 0

代入

x^{2} e^{1 - x} : 0

极小值 (0, 0)

将

x = 2

代入

x^{2} e^{1 - x} : \frac{4}{e}

极大值 (2, \frac{4}{e})

极小值 (0, 0), 极大值 (2, \frac{4}{e})

作图

流行的例子

extreme (3-x)(x-5)^2

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

extreme f(x,y)= 1/x+1/y-xy+3

e x t re m e f (x, y) = \frac{1}{x} + \frac{1}{y} - x y + 3

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

e x t re m e f (x) = x^{3} + y^{3} + 9 x^{2} - 9 y^{2} - 2

extreme f(x)=((x))/((6x+2)),5<= x<= 8

e x t re m e f (x) = \frac{( x )}{( 6 x + 2 )}, 5 \leq x \leq 8

extreme f(x,y)=(x-1)^3+(x-1)^2+(y+1)^2

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