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)=2sin(x)-x,0<= x<= 2pi

解答

极值点

f (x) = 2 sin (x) - x, 0 \leq x \leq 2 π

解答

极小值 (0, 0), 极大值 (\frac{π}{3}, 3 - \frac{π}{3}), 极小值 (\frac{5 π}{3}, - 3 - \frac{5 π}{3}), 极大值 (2 π, - 2 π)

求解步骤

找到临界点:

x = 0, x = \frac{π}{3}, x = \frac{5 π}{3}, x = 2 π

2 sin (x) - x, 0 \leq x \leq 2 π

的定义域

: 0 \leq x \leq 2 π

Find intervals:

递增

: 0 < x < \frac{π}{3},

递减

: \frac{π}{3} < x < \frac{5 π}{3},

递增

: \frac{5 π}{3} < x < 2 π

将极值点

x = 0

代入

2 sin (x) - x \Rightarrow y = 0

极小值 (0, 0)

将极值点

x = \frac{π}{3}

代入

2 sin (x) - x \Rightarrow y = 3 - \frac{π}{3}

极大值 (\frac{π}{3}, 3 - \frac{π}{3})

将极值点

x = \frac{5 π}{3}

代入

2 sin (x) - x \Rightarrow y = - 3 - \frac{5 π}{3}

极小值 (\frac{5 π}{3}, - 3 - \frac{5 π}{3})

将极值点

x = 2 π

代入

2 sin (x) - x \Rightarrow y = - 2 π

极大值 (2 π, - 2 π)

极小值 (0, 0), 极大值 (\frac{π}{3}, 3 - \frac{π}{3}), 极小值 (\frac{5 π}{3}, - 3 - \frac{5 π}{3}), 极大值 (2 π, - 2 π)

作图

流行的例子

extreme f(x)=8+6x-7x^2-4x^3

e x t re m e f (x) = 8 + 6 x - 7 x^{2} - 4 x^{3}

extreme f(x)=(20)/(3(2+x)^3)

e x t re m e f (x) = \frac{20}{3 ( 2 + x ) ^{3}}

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

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

extreme 2(x-1)(x^2+1)(3x^2-2x+1)

e x t re m e 2 (x - 1) (x^{2} + 1) (3 x^{2} - 2 x + 1)

extreme x^3+30x+128

e x t re m e x^{3} + 30 x + 128