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受欢迎的函数 >

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

解答

极值点

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

解答

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

x - 2 sin (x), 0 \leq x \leq 2 π

的定义域

: 0 \leq x \leq 2 π

Find intervals:

递减

: 0 < x < \frac{π}{3},

递增

: \frac{π}{3} < x < \frac{5 π}{3},

递减

: \frac{5 π}{3} < x < 2 π

将极值点

x = 0

代入

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

极大值 (0, 0)

将极值点

x = \frac{π}{3}

代入

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

极小值 (\frac{π}{3}, \frac{π}{3} - 3)

将极值点

x = \frac{5 π}{3}

代入

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

极大值 (\frac{5 π}{3}, \frac{5 π}{3} + 3)

将极值点

x = 2 π

代入

x - 2 sin (x) \Rightarrow y = 2 π

极小值 (2 π, 2 π)

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

作图

流行的例子

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