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 2x^3-3x^2-x+9

解答

极值点

2 x^{3} - 3 x^{2} - x + 9

解答

极大值 (\frac{3 - 15}{6}, \frac{5 15 - 18}{18} + 9), 极小值 (\frac{3 + 15}{6}, \frac{- 18 - 5 15}{18} + 9)

求解步骤

f^{'} (x) = 6 x^{2} - 6 x - 1

Find intervals:

递增

: - \infty < x < - \frac{5}{2 3} + \frac{1}{2},

递减

: - \frac{5}{2 3} + \frac{1}{2} < x < \frac{5}{2 3} + \frac{1}{2},

递增

: \frac{5}{2 3} + \frac{1}{2} < x < \infty

将

x = \frac{3 - 15}{6}

代入

2 x^{3} - 3 x^{2} - x + 9 : \frac{5 15 - 18}{18} + 9

极大值 (\frac{3 - 15}{6}, \frac{5 15 - 18}{18} + 9)

将

x = \frac{3 + 15}{6}

代入

2 x^{3} - 3 x^{2} - x + 9 : \frac{- 18 - 5 15}{18} + 9

极小值 (\frac{3 + 15}{6}, \frac{- 18 - 5 15}{18} + 9)

极大值 (\frac{3 - 15}{6}, \frac{5 15 - 18}{18} + 9), 极小值 (\frac{3 + 15}{6}, \frac{- 18 - 5 15}{18} + 9)

作图

流行的例子

extreme f(x)=(x-6)e^{-6x}

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

extreme 2t^{10}(4-t^2)^5

e x t re m e 2 t^{10} (4 - t^{2})^{5}

extreme f(x)=f(x,y)=-x^2-2y^2+xy+x+3y

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

extreme f(y)=x^3+y^3-27xy

e x t re m e f (y) = x^{3} + y^{3} - 27 x y

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

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