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)/(8x^2+1)

解答

极值点

\frac{x ^{2} - x}{8 x ^{2} + 1}

解答

极大值 (- \frac{1}{2}, \frac{1}{4}), 极小值 (\frac{1}{4}, - \frac{1}{8})

求解步骤

f^{'} (x) = \frac{8 x ^{2} + 2 x - 1}{( 8 x ^{2} + 1 ) ^{2}}

Find intervals:

递增

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

递减

: - \frac{1}{2} < x < \frac{1}{4},

递增

: \frac{1}{4} < x < \infty

将

x = - \frac{1}{2}

代入

\frac{x ^{2} - x}{8 x ^{2} + 1} : \frac{1}{4}

极大值 (- \frac{1}{2}, \frac{1}{4})

将

x = \frac{1}{4}

代入

\frac{x ^{2} - x}{8 x ^{2} + 1} : - \frac{1}{8}

极小值 (\frac{1}{4}, - \frac{1}{8})

极大值 (- \frac{1}{2}, \frac{1}{4}), 极小值 (\frac{1}{4}, - \frac{1}{8})

作图

流行的例子

extreme f(x)=y^x

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

extreme f(x)=2x^3+2y^2-6x-8y+14

e x t re m e f (x) = 2 x^{3} + 2 y^{2} - 6 x - 8 y + 14

extreme f(x)=2x^2-8[0.6]

e x t re m e f (x) = 2 x^{2} - 8 [0.6]

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

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

extreme f(x)=-x^4+2x^3+8x

e x t re m e f (x) = - x^{4} + 2 x^{3} + 8 x