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 2sin^2(x)

解答

极值点

2 sin^{2} (x)

解答

极小值 (πn, 0), 极大值 (\frac{π}{2} + πn, 2)

求解步骤

找到临界点:

x = πn, x = \frac{π}{2} + πn

2 sin^{2} (x)

的定义域

: - \infty < x < \infty

Find intervals:

递增

: πn < x < \frac{π}{2} + πn,

递减

: \frac{π}{2} + πn < x < π + πn

将极值点

x = πn

代入

2 sin^{2} (x) \Rightarrow y = 0

极小值 (πn, 0)

将极值点

x = \frac{π}{2} + πn

代入

2 sin^{2} (x) \Rightarrow y = 2

极大值 (\frac{π}{2} + πn, 2)

极小值 (πn, 0), 极大值 (\frac{π}{2} + πn, 2)

作图

流行的例子

extreme f(x,y)=x^2+x-3xy+y^3-5

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

extreme y=5-2x^2,-4<= x<= 2

e x t re m e y = 5 - 2 x^{2}, - 4 \leq x \leq 2

extreme f(x)=x^3-7/2 x^2+2x-5

e x t re m e f (x) = x^{3} - \frac{7}{2} x^{2} + 2 x - 5

extreme f(x)=(t^2-4)^3

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

extreme x/(x^2+16),0<= x<= 8

e x t re m e \frac{x}{x ^{2} + 16}, 0 \leq x \leq 8