题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140436-41484.png)
(I)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-48844.png)
(II)若不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-59258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-53131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-54884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-40754.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-48844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140438-20447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140438-55065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-40754.png)
解析
试题分析:本题主要考查导数的运算、利用导数研究函数的单调性、利用导数研究函数的极值与最值、恒成立问题等数学知识,考查综合分析问题解决问题的能力和计算能力,考查函数思想和分类讨论思想.第一问,首先求函数的定义域,利用
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140438-73615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140438-52690.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-51316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
试题解析:(I)函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-48844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-57224.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-77955.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-14560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140440-43444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140440-53516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140440-44658.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-48844.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140438-20447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140438-55065.png)
(II)(解法一)由已知
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-59258.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-54884.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140440-27486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140440-14911.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140441-53763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140441-34736.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140441-67004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140441-55557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-54884.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140442-44416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140442-63215.png)
由零点存在定理,存在
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140442-26418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140442-98777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140442-58416.png)
又函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140441-55557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-54884.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140443-90597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140443-39292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140443-89900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140443-39441.png)
从而当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140443-90597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140444-88550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140443-89900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140444-43031.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-54884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140444-84325.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140444-29305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-54884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140444-53479.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140442-26418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140445-39391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140437-40754.png)
解法二:由题意
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140445-92921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140445-96169.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140445-11095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140445-44237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140446-53393.png)
1.当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140446-79050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140446-48797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140446-86838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140446-32567.png)
2.当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140447-83456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140447-14325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140447-37478.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140439-71704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140447-37220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140447-39061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140448-94483.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140448-82777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140448-73477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140448-57698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140449-99196.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140449-72255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140449-16114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140449-89794.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140450-11547.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140409-58853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140409-58853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140409-45747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140409-58853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140409-96994.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140410-73696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140410-96980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140410-73289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140409-45747.png)
A.2 | B.3 | C.4 | D.5 |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140401-49210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140401-42388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140355-50906.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140325-96007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140325-25030.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140251-55307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140251-69998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140251-21277.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140252-84632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204140252-49854.png)
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