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受欢迎的函数 >

extreme sin(3x),-pi/4 <= x<= pi/3

解答

极值点

sin (3 x), - \frac{π}{4} \leq x \leq \frac{π}{3}

解答

极大值 (- \frac{π}{4}, - \frac{2}{2}), 极小值 (- \frac{π}{6}, - 1), 极大值 (\frac{π}{6}, 1), 极小值 (\frac{π}{3}, 0)

求解步骤

找到临界点:

x = - \frac{π}{4}, x = - \frac{π}{6}, x = \frac{π}{6}, x = \frac{π}{3}

sin (3 x), - \frac{π}{4} \leq x \leq \frac{π}{3}

的定义域

: - \frac{π}{4} \leq x \leq \frac{π}{3}

Find intervals:

递减

: - \frac{π}{4} < x < - \frac{π}{6},

递增

: - \frac{π}{6} < x < \frac{π}{6},

递减

: \frac{π}{6} < x < \frac{π}{3}

将极值点

x = - \frac{π}{4}

代入

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

极大值 (- \frac{π}{4}, - \frac{2}{2})

将极值点

x = - \frac{π}{6}

代入

sin (3 x) \Rightarrow y = - 1

极小值 (- \frac{π}{6}, - 1)

将极值点

x = \frac{π}{6}

代入

sin (3 x) \Rightarrow y = 1

极大值 (\frac{π}{6}, 1)

将极值点

x = \frac{π}{3}

代入

sin (3 x) \Rightarrow y = 0

极小值 (\frac{π}{3}, 0)

极大值 (- \frac{π}{4}, - \frac{2}{2}), 极小值 (- \frac{π}{6}, - 1), 极大值 (\frac{π}{6}, 1), 极小值 (\frac{π}{3}, 0)

作图

流行的例子

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