题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-71415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-57467.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-31818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-22911.png)
(2)若当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-10514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-78444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-22911.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-32097.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-95893.png)
解析
试题分析:解:(1)由题意可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-68523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020833-65092.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020833-44840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020833-33754.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020833-75514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-32097.png)
(2)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-10514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020834-34631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020834-28891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020834-83743.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020834-25958.png)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020834-96184.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-31818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-58595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-10998.png)
则当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-10514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-45913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-93281.png)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-15193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020836-24947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-31818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020836-87120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020836-58046.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020836-27586.png)
③ 当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020837-99099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-31818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-10998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020835-58595.png)
则当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-10514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020837-58457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020837-12464.png)
综上所述,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020831-22911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020832-95893.png)
点评:解决的关键是利用导数的符号确定单调性,进而确定函数的极值和最值,同时结合分类讨论的思想来得到函数的极值,求解参数的范围。易错点是不等式的恒成立问题,转化为函数的 最值得问题。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020826-39101.png)
(1)求f(x)的极小值; (2)若a、b>0,求证:lna-lnb≥1-
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020827-21422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020822-54275.png)
A.1,-1 | B. 3,-17 | C. 1,-17 | D.9,-19 |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020807-36954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020807-40541.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020807-16820.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020807-36334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020808-17718.png)
(2)在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020808-67321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020808-59535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020808-69394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020808-80946.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020809-87490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020809-18029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020809-54140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-40797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-59981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-77832.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-59981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-40797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-59981.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020800-17014.jpg)
A.1 | B.2 | C.3 | D.4 |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020752-20547.png)
A.极小值-1,极大值1 | B.极小值-2,极大值3 |
C.极小值-1,极大值3 | D.极小值-2,极大值2 |
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