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受欢迎的函数 >

extreme y=-2+5sin(pi/(12)(x-2))

解答

极值点

y = - 2 + 5 sin (\frac{π}{12} (x - 2))

解答

极大值 (8 + 24 n, 3), 极小值 (20 + 24 n, - 7)

求解步骤

找到临界点:

x = 8 + 24 n, x = 20 + 24 n

- 2 + 5 sin (\frac{π}{12} (x - 2))

的定义域

: - \infty < x < \infty

Find intervals:

递增

: 24 n \leq x < 8 + 24 n,

递减

: 8 + 24 n < x < 20 + 24 n,

递增

: 20 + 24 n < x < 24 + 24 n

将极值点

x = 8 + 24 n

代入

- 2 + 5 sin (\frac{π}{12} (x - 2)) \Rightarrow y = 3

极大值 (8 + 24 n, 3)

将极值点

x = 20 + 24 n

代入

- 2 + 5 sin (\frac{π}{12} (x - 2)) \Rightarrow y = - 7

极小值 (20 + 24 n, - 7)

极大值 (8 + 24 n, 3), 极小值 (20 + 24 n, - 7)

作图

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