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受欢迎的函数 >

extreme f(x)=((sqrt(3)-cos(θ))/(sin(θ)))

解答

极值点

f (x) = (\frac{3 - cos ( θ )}{sin ( θ )})

解答

极小值 (arccos (\frac{1}{3}) + 2 πn, 2), 极大值 (2 π - arccos (\frac{1}{3}) + 2 πn, - 2)

求解步骤

找到临界点:

θ = arccos (\frac{1}{3}) + 2 πn, θ = 2 π - arccos (\frac{1}{3}) + 2 πn

\frac{3 - cos ( θ )}{sin ( θ )}

的定义域

: 2 πn < θ < π + 2 πn or π + 2 πn < θ < 2 π + 2 πn

Find intervals:

递减

: 2 πn < θ < arccos (\frac{1}{3}) + 2 πn,

递增

: arccos (\frac{1}{3}) + 2 πn < θ < π + 2 πn,

递增

: π + 2 πn < θ < 2 π - arccos (\frac{1}{3}) + 2 πn,

递减

: 2 π - arccos (\frac{1}{3}) + 2 πn < θ < 2 π + 2 πn

将极值点

x = arccos (\frac{1}{3}) + 2 πn

代入

\frac{3 - cos ( θ )}{sin ( θ )} \Rightarrow y = 2

极小值 (arccos (\frac{1}{3}) + 2 πn, 2)

将极值点

x = 2 π - arccos (\frac{1}{3}) + 2 πn

代入

\frac{3 - cos ( θ )}{sin ( θ )} \Rightarrow y = - 2

极大值 (2 π - arccos (\frac{1}{3}) + 2 πn, - 2)

极小值 (arccos (\frac{1}{3}) + 2 πn, 2), 极大值 (2 π - arccos (\frac{1}{3}) + 2 πn, - 2)

作图

流行的例子

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