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受欢迎的函数 >

extreme f(x)=2-4(sin^2(x))

解答

极值点

f (x) = 2 - 4 (sin^{2} (x))

解答

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

求解步骤

找到临界点:

x = πn, x = \frac{π}{2} + πn

2 - 4 sin^{2} (x)

的定义域

: - \infty < x < \infty

Find intervals:

递减

: πn < x < \frac{π}{2} + πn,

递增

: \frac{π}{2} + πn < x < π + πn

将极值点

x = πn

代入

2 - 4 sin^{2} (x) \Rightarrow y = 2

极大值 (πn, 2)

将极值点

x = \frac{π}{2} + πn

代入

2 - 4 sin^{2} (x) \Rightarrow y = - 2

极小值 (\frac{π}{2} + πn, - 2)

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

作图

流行的例子

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