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受欢迎的函数 >

extreme (10000)/(2.5cos(x)+sin(x))

解答

极值点

\frac{10000}{2.5 cos ( x ) + sin ( x )}

解答

极小值 (arctan (\frac{2}{5}) + 2 πn, 3713.90676 \dots), 极大值 (arctan (\frac{2}{5}) + π + 2 πn, - 3713.90676 \dots)

求解步骤

找到临界点:

x = arctan (\frac{2}{5}) + 2 πn, x = arctan (\frac{2}{5}) + π + 2 πn

\frac{10000}{2.5 cos ( x ) + sin ( x )}

的定义域

: 2 πn \leq x < - 1.19028 \dots + π + 2 πn or - 1.19028 \dots + π + 2 πn < x < 5.09289 \dots + 2 πn or 5.09289 \dots + 2 πn < x < 2 π + 2 πn

Find intervals:

递减

: 2 πn \leq x < arctan (\frac{2}{5}) + 2 πn,

递增

: arctan (\frac{2}{5}) + 2 πn < x < - 1.19028 \dots + π + 2 πn,

递增

: - 1.19028 \dots + π + 2 πn < x < arctan (\frac{2}{5}) + π + 2 πn,

递减

: arctan (\frac{2}{5}) + π + 2 πn < x < 5.09289 \dots + 2 πn,

递减

: 5.09289 \dots + 2 πn < x < 2 π + 2 πn

将极值点

x = arctan (\frac{2}{5}) + 2 πn

代入

\frac{10000}{2.5 cos ( x ) + sin ( x )} \Rightarrow y = 3713.90676 \dots

极小值 (arctan (\frac{2}{5}) + 2 πn, 3713.90676 \dots)

将极值点

x = arctan (\frac{2}{5}) + π + 2 πn

代入

\frac{10000}{2.5 cos ( x ) + sin ( x )} \Rightarrow y = - 3713.90676 \dots

极大值 (arctan (\frac{2}{5}) + π + 2 πn, - 3713.90676 \dots)

极小值 (arctan (\frac{2}{5}) + 2 πn, 3713.90676 \dots), 极大值 (arctan (\frac{2}{5}) + π + 2 πn, - 3713.90676 \dots)

作图

流行的例子

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