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)=(2x)/(x^2+16),-8<= x<= 8

解答

极值点

F (x) = \frac{2 x}{x ^{2} + 16}, - 8 \leq x \leq 8

解答

极大值 (- 8, - \frac{1}{5}), 极小值 (- 4, - \frac{1}{4}), 极大值 (4, \frac{1}{4}), 极小值 (8, \frac{1}{5})

求解步骤

找到临界点:

x = - 8, x = - 4, x = 4, x = 8

\frac{2 x}{x ^{2} + 16}, - 8 \leq x \leq 8

的定义域

: - 8 \leq x \leq 8

Find intervals:

递减

: - 8 < x < - 4,

递增

: - 4 < x < 4,

递减

: 4 < x < 8

将极值点

x = - 8

代入

\frac{2 x}{x ^{2} + 16} \Rightarrow y = - \frac{1}{5}

极大值 (- 8, - \frac{1}{5})

将极值点

x = - 4

代入

\frac{2 x}{x ^{2} + 16} \Rightarrow y = - \frac{1}{4}

极小值 (- 4, - \frac{1}{4})

将极值点

x = 4

代入

\frac{2 x}{x ^{2} + 16} \Rightarrow y = \frac{1}{4}

极大值 (4, \frac{1}{4})

将极值点

x = 8

代入

\frac{2 x}{x ^{2} + 16} \Rightarrow y = \frac{1}{5}

极小值 (8, \frac{1}{5})

极大值 (- 8, - \frac{1}{5}), 极小值 (- 4, - \frac{1}{4}), 极大值 (4, \frac{1}{4}), 极小值 (8, \frac{1}{5})

作图

流行的例子

extreme-(9/2)^2-7^2+9/2-14+3

e x t re m e - (\frac{9}{2})^{2} - 7^{2} + \frac{9}{2} - 14 + 3

extreme x(sqrt(8-x^2))

e x t re m e x (8 - x^{2})

extreme f(x)=f(x)=-8x^2-144x+6

e x t re m e f (x) = f (x) = - 8 x^{2} - 144 x + 6

extreme f(x)=x^3-3x[0.3]

e x t re m e f (x) = x^{3} - 3 x [0.3]

extreme f(x)=(4860)/x+18x+731856

e x t re m e f (x) = \frac{4860}{x} + 18 x + 731856