設(shè)函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119023091045.png)
(
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902325399.png)
)
(1)寫出函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902341447.png)
的定義域;(2)討論函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902341447.png)
的單調(diào)性.
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902372543.png)
(2)當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119023871072.png)
有兩個(gè)零點(diǎn),
且當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119024191430.png)
內(nèi)為增函數(shù);
當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902434899.png)
內(nèi)為減函數(shù); 2
②當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119024811151.png)
內(nèi)為增函數(shù); 2
③當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902497933.png)
內(nèi)為增函數(shù); 2
④當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902512433.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902528481.png)
在定義域內(nèi)有唯一零點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902543300.png)
,當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902559879.png)
內(nèi)為增函數(shù),當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902575380.png)
時(shí)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902590759.png)
內(nèi)為減函數(shù)
試題分析:解:(1)函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902341447.png)
的定義域?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902372543.png" style="vertical-align:middle;" /> 2
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119026211132.png)
當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119026371206.png)
的判別式,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119026531082.png)
①當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119023871072.png)
有兩個(gè)零點(diǎn),
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119026842419.png)
且當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119026991781.png)
內(nèi)為增函數(shù);
當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119027151116.png)
內(nèi)為減函數(shù); 2
②當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119027151840.png)
內(nèi)為增函數(shù); 2
③當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119027311540.png)
內(nèi)為增函數(shù); 2
④當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119027461684.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119027621767.png)
在定義域內(nèi)有唯一零點(diǎn)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902543300.png)
,
當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240119027931063.png)
內(nèi)為增函數(shù),當(dāng)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902575380.png)
時(shí)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824011902824966.png)
內(nèi)為減函數(shù)。2
點(diǎn)評:本試題主要是考查了分類討論思想來秋季誒函數(shù)的零點(diǎn),進(jìn)而得到單調(diào)性的判定,屬于中檔題。
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