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受欢迎的函数 >

extreme f(x)=6sin^2(x)+6sin(x)

解答

极值点

f (x) = 6 sin^{2} (x) + 6 sin (x)

解答

极大值 (\frac{π}{2} + 2 πn, 12), 极小值 (\frac{7 π}{6} + 2 πn, - \frac{3}{2}), 极大值 (\frac{3 π}{2} + 2 πn, 0), 极小值 (\frac{11 π}{6} + 2 πn, - \frac{3}{2})

求解步骤

找到临界点:

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{11 π}{6} + 2 πn

6 sin^{2} (x) + 6 sin (x)

的定义域

: - \infty < x < \infty

Find intervals:

递增

: 2 πn \leq x < \frac{π}{2} + 2 πn,

递减

: \frac{π}{2} + 2 πn < x < \frac{7 π}{6} + 2 πn,

递增

: \frac{7 π}{6} + 2 πn < x < \frac{3 π}{2} + 2 πn,

递减

: \frac{3 π}{2} + 2 πn < x < \frac{11 π}{6} + 2 πn,

递增

: \frac{11 π}{6} + 2 πn < x < 2 π + 2 πn

将极值点

x = \frac{π}{2} + 2 πn

代入

6 sin^{2} (x) + 6 sin (x) \Rightarrow y = 12

极大值 (\frac{π}{2} + 2 πn, 12)

将极值点

x = \frac{7 π}{6} + 2 πn

代入

6 sin^{2} (x) + 6 sin (x) \Rightarrow y = - \frac{3}{2}

极小值 (\frac{7 π}{6} + 2 πn, - \frac{3}{2})

将极值点

x = \frac{3 π}{2} + 2 πn

代入

6 sin^{2} (x) + 6 sin (x) \Rightarrow y = 0

极大值 (\frac{3 π}{2} + 2 πn, 0)

将极值点

x = \frac{11 π}{6} + 2 πn

代入

6 sin^{2} (x) + 6 sin (x) \Rightarrow y = - \frac{3}{2}

极小值 (\frac{11 π}{6} + 2 πn, - \frac{3}{2})

极大值 (\frac{π}{2} + 2 πn, 12), 极小值 (\frac{7 π}{6} + 2 πn, - \frac{3}{2}), 极大值 (\frac{3 π}{2} + 2 πn, 0), 极小值 (\frac{11 π}{6} + 2 πn, - \frac{3}{2})

作图

流行的例子

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