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受欢迎的函数 >

extreme 2sec(t)+tan(t)

解答

极值点

2 sec (t) + tan (t)

解答

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

求解步骤

找到临界点:

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

2 sec (t) + tan (t)

的定义域

: 2 πn \leq t < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < t < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < t < 2 π + 2 πn

Find intervals:

递增

: 2 πn \leq t < \frac{π}{2} + 2 πn,

递增

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

递减

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

递减

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

递增

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

将极值点

x = \frac{7 π}{6} + 2 πn

代入

2 sec (t) + tan (t) \Rightarrow y = - 3

极大值 (\frac{7 π}{6} + 2 πn, - 3)

将极值点

x = \frac{11 π}{6} + 2 πn

代入

2 sec (t) + tan (t) \Rightarrow y = 3

极小值 (\frac{11 π}{6} + 2 πn, 3)

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

作图

流行的例子

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extreme f(x,y)=x^2+4y^2-2ln(xy)

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