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受欢迎的函数 >

extreme f(x)=6sin(x)+cot(x)

解答

极值点

f (x) = 6 sin (x) + cot (x)

解答

极小值 (0.44406 \dots + 2 πn, 4.67960 \dots), 极大值 (1.39820 \dots + 2 πn, 6.08518 \dots), 极小值 (4.88497 \dots + 2 πn, - 6.08518 \dots), 极大值 (5.83912 \dots + 2 πn, - 4.67960 \dots)

求解步骤

找到临界点:

x = 0.44406 \dots + 2 πn, x = 1.39820 \dots + 2 πn, x = 4.88497 \dots + 2 πn, x = 5.83912 \dots + 2 πn

6 sin (x) + cot (x)

的定义域

: 2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Find intervals:

递减

: 2 πn < x < 0.44406 \dots + 2 πn,

递增

: 0.44406 \dots + 2 πn < x < 1.39820 \dots + 2 πn,

递减

: 1.39820 \dots + 2 πn < x < π + 2 πn,

递减

: π + 2 πn < x < 4.88497 \dots + 2 πn,

递增

: 4.88497 \dots + 2 πn < x < 5.83912 \dots + 2 πn,

递减

: 5.83912 \dots + 2 πn < x < 2 π + 2 πn

将极值点

x = 0.44406 \dots + 2 πn

代入

6 sin (x) + cot (x) \Rightarrow y = 4.67960 \dots

极小值 (0.44406 \dots + 2 πn, 4.67960 \dots)

将极值点

x = 1.39820 \dots + 2 πn

代入

6 sin (x) + cot (x) \Rightarrow y = 6.08518 \dots

极大值 (1.39820 \dots + 2 πn, 6.08518 \dots)

将极值点

x = 4.88497 \dots + 2 πn

代入

6 sin (x) + cot (x) \Rightarrow y = - 6.08518 \dots

极小值 (4.88497 \dots + 2 πn, - 6.08518 \dots)

将极值点

x = 5.83912 \dots + 2 πn

代入

6 sin (x) + cot (x) \Rightarrow y = - 4.67960 \dots

极大值 (5.83912 \dots + 2 πn, - 4.67960 \dots)

极小值 (0.44406 \dots + 2 πn, 4.67960 \dots), 极大值 (1.39820 \dots + 2 πn, 6.08518 \dots), 极小值 (4.88497 \dots + 2 πn, - 6.08518 \dots), 极大值 (5.83912 \dots + 2 πn, - 4.67960 \dots)

作图

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