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)= x/(sqrt(2))-2sin(x/2)

解答

极值点

f (x) = \frac{x}{2} - 2 sin (\frac{x}{2})

解答

极小值 (\frac{π}{2} + 4 πn, \frac{π + 8 πn}{2 2} - 2 sin (\frac{π + 8 πn}{4})), 极大值 (\frac{7 π}{2} + 4 πn, \frac{7 π + 8 πn}{2 2} - 2 sin (\frac{7 π + 8 πn}{4}))

求解步骤

找到临界点:

x = \frac{π}{2} + 4 πn, x = \frac{7 π}{2} + 4 πn

\frac{x}{2} - 2 sin (\frac{x}{2})

的定义域

: - \infty < x < \infty

Find intervals:

递减

: 4 πn \leq x < \frac{π}{2} + 4 πn,

递增

: \frac{π}{2} + 4 πn < x < \frac{7 π}{2} + 4 πn,

递减

: \frac{7 π}{2} + 4 πn < x < 4 π + 4 πn

将极值点

x = \frac{π}{2} + 4 πn

代入

\frac{x}{2} - 2 sin (\frac{x}{2}) \Rightarrow y = \frac{π + 8 πn}{2 2} - 2 sin (\frac{π + 8 πn}{4})

极小值 (\frac{π}{2} + 4 πn, \frac{π + 8 πn}{2 2} - 2 sin (\frac{π + 8 πn}{4}))

将极值点

x = \frac{7 π}{2} + 4 πn

代入

\frac{x}{2} - 2 sin (\frac{x}{2}) \Rightarrow y = \frac{7 π + 8 πn}{2 2} - 2 sin (\frac{7 π + 8 πn}{4})

极大值 (\frac{7 π}{2} + 4 πn, \frac{7 π + 8 πn}{2 2} - 2 sin (\frac{7 π + 8 πn}{4}))

极小值 (\frac{π}{2} + 4 πn, \frac{π + 8 πn}{2 2} - 2 sin (\frac{π + 8 πn}{4})), 极大值 (\frac{7 π}{2} + 4 πn, \frac{7 π + 8 πn}{2 2} - 2 sin (\frac{7 π + 8 πn}{4}))

作图

流行的例子

e x t re m e x - x^{3}

extreme f(x)=2x-3\sqrt[3]{x^2}

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

extreme f(x)=x^2+4x+16

e x t re m e f (x) = x^{2} + 4 x + 16

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

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

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

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