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^3-4x^2)/(x^2+1)

解答

极值点

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

解答

极大值 (0, 0), 极小值 (1.51274 \dots, - 1.73088 \dots)

求解步骤

找到临界点:

x = 0, x \approx 1.51274 \dots

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

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < 1.51274 \dots,

递增

: 1.51274 \dots < x < \infty

将极值点

x = 0

代入

\frac{x ^{3} - 4 x ^{2}}{x ^{2} + 1} \Rightarrow y = 0

极大值 (0, 0)

将极值点

x = 1.51274 \dots

代入

\frac{x ^{3} - 4 x ^{2}}{x ^{2} + 1} \Rightarrow y = - 1.73088 \dots

极小值 (1.51274 \dots, - 1.73088 \dots)

极大值 (0, 0), 极小值 (1.51274 \dots, - 1.73088 \dots)

作图

流行的例子

extreme f(x)=10+5x-x^2

e x t re m e f (x) = 10 + 5 x - x^{2}

extreme f(x)=2x^2nx-19x^2

e x t re m e f (x) = 2 x^{2} n x - 19 x^{2}

extreme f(x,y,z)=-x^2-3y^2+4x-6y-5

e x t re m e f (x, y, z) = - x^{2} - 3 y^{2} + 4 x - 6 y - 5

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

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

extreme f(z)=x^2-y^2-2x+4y+6

e x t re m e f (z) = x^{2} - y^{2} - 2 x + 4 y + 6