已知函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705558965.png)
,設(shè)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705573431.png)
(1)試確定
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705589267.png)
的取值范圍,使得函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705605495.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705620434.png)
上為單調(diào)函數(shù);
(2)求函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705605495.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705620434.png)
上的最小值.
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705667528.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705683438.png)
試題分析:(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705698740.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705714447.png)
的單調(diào)遞增區(qū)間為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705761725.png)
,單調(diào)遞減區(qū)間
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705761459.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705667528.png)
(2)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705807508.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705714447.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705839434.png)
上單調(diào)遞增,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705854955.png)
當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705870449.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705714447.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705901527.png)
上單調(diào)遞增,在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705901490.png)
上單調(diào)遞減
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705854955.png)
當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705948356.png)
時,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705714447.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705979761.png)
上單調(diào)遞增,在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705761459.png)
上單調(diào)遞減,
同理
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705917863.png)
,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705854955.png)
綜上:當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705714447.png)
在
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705839434.png)
上的最小值為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824005705683438.png)
點評:對于導(dǎo)數(shù)在研究函數(shù)中的運用,一般考查了導(dǎo)數(shù)的符號與函數(shù)單調(diào)性的關(guān)系,以及函數(shù)的最值,屬于基礎(chǔ)題。
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