题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115211-56418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115211-61887.png)
(Ⅰ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115211-86594.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115211-44557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-80706.png)
(Ⅱ)若存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-46189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-14501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-54474.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-70678.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-56436.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115211-44557.png)
第二问中,利用存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-46189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-14501.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-11320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-68087.png)
解:(1)
①
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-51345.png)
(2)不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115212-11320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-49728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-51960.png)
转化为存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-54111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-73646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-51960.png)
即不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115214-72476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-73646.png)
即不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115214-79132.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-73646.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115214-65836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115214-42762.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115214-73757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115214-85797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-73646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115215-88327.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115215-99946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115213-73646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115215-62330.png)
故存在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115215-57508.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115215-70966.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115215-48162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115216-33013.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115216-26475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115216-94581.png)
从而
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115216-84900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115217-13069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115217-39139.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115217-65607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115217-49258.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115217-43640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115218-20081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115218-19937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115218-90077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115218-21402.png)
故使命题成立的正整数m的最大值为5
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115201-19726.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115202-50453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115202-70201.png)
(Ⅱ)判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115202-76498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115151-92874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115151-30807.png)
(Ⅰ)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115151-45505.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115152-58496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115146-86480.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115146-27633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115146-27633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115125-46257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115125-44701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115125-67097.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115126-97071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115126-35648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115126-14893.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115126-54137.png)
(2)求证:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115126-14706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115126-99947.png)
(3)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115127-90439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115127-40155.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115127-62332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115127-46744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115127-62190.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115127-35002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018115128-76874.png)
(Ⅰ)若曲线y=f(x)在点(1,f(1))处的切线平行于x轴,求函数f(x)的单调区间;
(Ⅱ)试确定a的取值范围,使得曲线y=f(x)上存在唯一的点P,曲线在该点处的切线与曲线只有一个公共点P
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