已知函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136367781274.png)
(1)將函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636793447.png)
化簡成
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136368241440.png)
的形式;
(2)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636793447.png)
的單調(diào)遞減區(qū)間;
(3)求函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636793447.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636887686.png)
上的最大值和最小值.
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136369181043.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636934959.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636965565.png)
(3)當(dāng)x=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636980494.png)
時(shí),f(x)有最小值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636996556.png)
;當(dāng)x=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637027413.png)
時(shí),f(x)有最大值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637043493.png)
.
試題分析:解:(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136370741281.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136370901203.png)
4分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136371211048.png)
…6分
(2) 令
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136371361058.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637168445.png)
解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637183985.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637230473.png)
單調(diào)遞減區(qū)間為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636934959.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636965565.png)
. 8分
(3)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637277729.png)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240136373391241.png)
11分
故當(dāng)x=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636980494.png)
時(shí),f(x)有最小值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013636996556.png)
;當(dāng)x=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637027413.png)
時(shí),f(x)有最大值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824013637043493.png)
. 12分
點(diǎn)評:主要是考查了三角函數(shù)的性質(zhì)和二倍角公式的運(yùn)用,屬于中檔題。
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