zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的函数 >

extreme f(x)=xe^{-(x^2)/(32)}[-3.8]

解答

极值点

f (x) = x e^{- \frac{x ^{2}}{32}} [- 3.8]

解答

极大值 (- \frac{1}{0.062 5 ^{\frac{1}{2}}}, 9.21926 \dots), 极小值 (\frac{1}{0.062 5 ^{\frac{1}{2}}}, - 9.21926 \dots)

求解步骤

找到临界点:

x = - \frac{1}{0.062 5 ^{\frac{1}{2}}}, x = \frac{1}{0.062 5 ^{\frac{1}{2}}}

x e^{- \frac{x ^{2}}{32}} [- 3.8]

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < - \frac{1}{0.062 5 ^{\frac{1}{2}}},

递减

: - \frac{1}{0.062 5 ^{\frac{1}{2}}} < x < \frac{1}{0.062 5 ^{\frac{1}{2}}},

递增

: \frac{1}{0.062 5 ^{\frac{1}{2}}} < x < \infty

将极值点

x = - \frac{1}{0.062 5 ^{\frac{1}{2}}}

代入

x e^{- \frac{x ^{2}}{32}} [- 3.8] \Rightarrow y = 9.21926 \dots

极大值 (- \frac{1}{0.062 5 ^{\frac{1}{2}}}, 9.21926 \dots)

将极值点

x = \frac{1}{0.062 5 ^{\frac{1}{2}}}

代入

x e^{- \frac{x ^{2}}{32}} [- 3.8] \Rightarrow y = - 9.21926 \dots

极小值 (\frac{1}{0.062 5 ^{\frac{1}{2}}}, - 9.21926 \dots)

极大值 (- \frac{1}{0.062 5 ^{\frac{1}{2}}}, 9.21926 \dots), 极小值 (\frac{1}{0.062 5 ^{\frac{1}{2}}}, - 9.21926 \dots)

作图

流行的例子

extreme U(X,Y)=2X+5Y

e x t re m e U (X, Y) = 2 X + 5 Y

extreme f(x,y)=5x^2-5y^2

e x t re m e f (x, y) = 5 x^{2} - 5 y^{2}

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

e x t re m e f (x) = 3 x^{4} - x^{2} + 4 x - 2

extreme f(x)=x^4+8x^3+3

e x t re m e f (x) = x^{4} + 8 x^{3} + 3

extreme f(x,y)=3x+4y+1

e x t re m e f (x, y) = 3 x + 4 y + 1