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受欢迎的函数 >

extreme y=sin(x)cos(x)

解答

极值点

y = sin (x) cos (x)

解答

极大值 (\frac{π}{4} + πn, \frac{1}{2}), 极小值 (\frac{3 π}{4} + πn, - \frac{1}{2})

求解步骤

找到临界点:

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

sin (x) cos (x)

的定义域

: - \infty < x < \infty

Find intervals:

递增

: πn \leq x < \frac{π}{4} + πn,

递减

: \frac{π}{4} + πn < x < \frac{3 π}{4} + πn,

递增

: \frac{3 π}{4} + πn < x < π + πn

将极值点

x = \frac{π}{4} + πn

代入

sin (x) cos (x) \Rightarrow y = \frac{1}{2}

极大值 (\frac{π}{4} + πn, \frac{1}{2})

将极值点

x = \frac{3 π}{4} + πn

代入

sin (x) cos (x) \Rightarrow y = - \frac{1}{2}

极小值 (\frac{3 π}{4} + πn, - \frac{1}{2})

极大值 (\frac{π}{4} + πn, \frac{1}{2}), 极小值 (\frac{3 π}{4} + πn, - \frac{1}{2})

作图

流行的例子

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