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)=15x^2-15x^4

解答

极值点

f (x) = 15 x^{2} - 15 x^{4}

解答

极大值 (- \frac{1}{2}, \frac{15}{4}), 极小值 (0, 0), 极大值 (\frac{1}{2}, \frac{15}{4})

求解步骤

f^{'} (x) = 30 x - 60 x^{3}

Find intervals:

递增

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

递减

: - \frac{1}{2} < x < 0,

递增

: 0 < x < \frac{1}{2},

递减

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

将

x = - \frac{1}{2}

代入

15 x^{2} - 15 x^{4} : \frac{15}{4}

极大值 (- \frac{1}{2}, \frac{15}{4})

将

x = 0

代入

15 x^{2} - 15 x^{4} : 0

极小值 (0, 0)

将

x = \frac{1}{2}

代入

15 x^{2} - 15 x^{4} : \frac{15}{4}

极大值 (\frac{1}{2}, \frac{15}{4})

极大值 (- \frac{1}{2}, \frac{15}{4}), 极小值 (0, 0), 极大值 (\frac{1}{2}, \frac{15}{4})

作图

流行的例子

extreme 6x^3-9x^2-216x+9

e x t re m e 6 x^{3} - 9 x^{2} - 216 x + 9

extreme f(x)=(x^4)/4+5/3 x^3-5x^2-50x+1

e x t re m e f (x) = \frac{x ^{4}}{4} + \frac{5}{3} x^{3} - 5 x^{2} - 50 x + 1

extreme f(x,y)= 1/2 x^2+y^3-xy

e x t re m e f (x, y) = \frac{1}{2} x^{2} + y^{3} - x y

extreme f(x)=2x^2-8x+2(0.5)

e x t re m e f (x) = 2 x^{2} - 8 x + 2 (0.5)

extreme f(xy)=4-x^2-2y^2

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