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)=(7x)/(x^2+9),0<= x<= 9

解答

极值点

f (x) = \frac{7 x}{x ^{2} + 9}, 0 \leq x \leq 9

解答

极小值 (0, 0), 极大值 (3, \frac{7}{6}), 极小值 (9, \frac{7}{10})

求解步骤

找到临界点:

x = 0, x = 3, x = 9

\frac{7 x}{x ^{2} + 9}, 0 \leq x \leq 9

的定义域

: 0 \leq x \leq 9

Find intervals:

递增

: 0 < x < 3,

递减

: 3 < x < 9

将极值点

x = 0

代入

\frac{7 x}{x ^{2} + 9} \Rightarrow y = 0

极小值 (0, 0)

将极值点

x = 3

代入

\frac{7 x}{x ^{2} + 9} \Rightarrow y = \frac{7}{6}

极大值 (3, \frac{7}{6})

将极值点

x = 9

代入

\frac{7 x}{x ^{2} + 9} \Rightarrow y = \frac{7}{10}

极小值 (9, \frac{7}{10})

极小值 (0, 0), 极大值 (3, \frac{7}{6}), 极小值 (9, \frac{7}{10})

作图

流行的例子

extreme 2x^3+4x^2-1

e x t re m e 2 x^{3} + 4 x^{2} - 1

extreme f(x)=x*(ln(x))^5

e x t re m e f (x) = x \cdot (ln (x))^{5}

extreme f(x,y)=40000x+30000y-8x^2-15y^2-10xy

e x t re m e f (x, y) = 40000 x + 30000 y - 8 x^{2} - 15 y^{2} - 10 x y

extreme f(x)=e^{x^3-3x}

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

extreme f(x)=x+(30)/x

e x t re m e f (x) = x + \frac{30}{x}