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)=(ln(x))/(8x),1<= x<= 4

解答

极值点

f (x) = \frac{ln ( x )}{8 x}, 1 \leq x \leq 4

解答

极小值 (1, 0), 极大值 (e, \frac{1}{8 e}), 极小值 (4, \frac{ln ( 2 )}{16})

求解步骤

找到临界点:

x = 1, x = e, x = 4

\frac{ln ( x )}{8 x}, 1 \leq x \leq 4

的定义域

: 1 \leq x \leq 4

Find intervals:

递增

: 1 < x < e,

递减

: e < x < 4

将极值点

x = 1

代入

\frac{ln ( x )}{8 x} \Rightarrow y = 0

极小值 (1, 0)

将极值点

x = e

代入

\frac{ln ( x )}{8 x} \Rightarrow y = \frac{1}{8 e}

极大值 (e, \frac{1}{8 e})

将极值点

x = 4

代入

\frac{ln ( x )}{8 x} \Rightarrow y = \frac{ln ( 2 )}{16}

极小值 (4, \frac{ln ( 2 )}{16})

极小值 (1, 0), 极大值 (e, \frac{1}{8 e}), 极小值 (4, \frac{ln ( 2 )}{16})

作图

流行的例子

extreme f(x)=(1+3x)/(sqrt(4+5x^2))

e x t re m e f (x) = \frac{1 + 3 x}{4 + 5 x ^{2}}

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

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

extreme f(x)=(2x^2+1)^2

e x t re m e f (x) = (2 x^{2} + 1)^{2}

extreme f(x,y)=(100)/(1+x^2+y^2)

e x t re m e f (x, y) = \frac{100}{1 + x ^{2} + y ^{2}}

extreme f(x)= 1/6 x^3-x^2+6x+11

e x t re m e f (x) = \frac{1}{6} x^{3} - x^{2} + 6 x + 11