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 (x^2+x)/(x-1)

解答

极值点

\frac{x ^{2} + x}{x - 1}

解答

极大值 (1 - 2, \frac{3 2 - 4}{2}), 极小值 (1 + 2, \frac{4 + 3 2}{2})

求解步骤

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

Find intervals:

递增

: - \infty < x < 1 - 2,

递减

: 1 - 2 < x < 1,

递减

: 1 < x < 1 + 2,

递增

: 1 + 2 < x < \infty

将

x = 1 - 2

代入

\frac{x ^{2} + x}{x - 1} : \frac{3 2 - 4}{2}

极大值 (1 - 2, \frac{3 2 - 4}{2})

将

x = 1 + 2

代入

\frac{x ^{2} + x}{x - 1} : \frac{4 + 3 2}{2}

极小值 (1 + 2, \frac{4 + 3 2}{2})

极大值 (1 - 2, \frac{3 2 - 4}{2}), 极小值 (1 + 2, \frac{4 + 3 2}{2})

作图

流行的例子

extreme (ln(x))/(6x)

e x t re m e \frac{ln ( x )}{6 x}

extreme h(x)=-6x^3+18x^2+3

e x t re m e h (x) = - 6 x^{3} + 18 x^{2} + 3

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

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

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})