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受欢迎的函数 >

extreme x-2sin(x)(0.2pi)

解答

极值点

x - 2 sin (x) (0.2 π)

解答

极小值 (arccos (0.79577 \dots) + 2 πn, 0.65051 \dots + 6.28318 \dots n - 1.25663 \dots sin (0.65051 \dots + 6.28318 \dots n)), 极大值 (2 π - arccos (0.79577 \dots) + 2 πn, 6.28318 \dots n + 5.63267 \dots - 1.25663 \dots sin (6.28318 \dots n + 5.63267 \dots))

求解步骤

找到临界点:

x = arccos (0.79577 \dots) + 2 πn, x = 2 π - arccos (0.79577 \dots) + 2 πn

x - 2 sin (x) 0.2 π

的定义域

: - \infty < x < \infty

Find intervals:

递减

: 6.28318 \dots n \leq x < arccos (0.79577 \dots) + 2 πn,

递增

: arccos (0.79577 \dots) + 2 πn < x < 2 π - arccos (0.79577 \dots) + 2 πn,

递减

: 2 π - arccos (0.79577 \dots) + 2 πn < x < 6.28318 \dots + 6.28318 \dots n

将极值点

x = arccos (0.79577 \dots) + 2 πn

代入

x - 2 sin (x) 0.2 π \Rightarrow y = 0.65051 \dots + 6.28318 \dots n - 1.25663 \dots sin (0.65051 \dots + 6.28318 \dots n)

极小值 (arccos (0.79577 \dots) + 2 πn, 0.65051 \dots + 6.28318 \dots n - 1.25663 \dots sin (0.65051 \dots + 6.28318 \dots n))

将极值点

x = 2 π - arccos (0.79577 \dots) + 2 πn

代入

x - 2 sin (x) 0.2 π \Rightarrow y = 6.28318 \dots n + 5.63267 \dots - 1.25663 \dots sin (6.28318 \dots n + 5.63267 \dots)

极大值 (2 π - arccos (0.79577 \dots) + 2 πn, 6.28318 \dots n + 5.63267 \dots - 1.25663 \dots sin (6.28318 \dots n + 5.63267 \dots))

极小值 (arccos (0.79577 \dots) + 2 πn, 0.65051 \dots + 6.28318 \dots n - 1.25663 \dots sin (0.65051 \dots + 6.28318 \dots n)), 极大值 (2 π - arccos (0.79577 \dots) + 2 πn, 6.28318 \dots n + 5.63267 \dots - 1.25663 \dots sin (6.28318 \dots n + 5.63267 \dots))

作图

流行的例子

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