题目
题型:山东省模拟题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071056-71656.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071057-64813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071057-10900.png)
(Ⅱ)讨论函数f(x)的单调性;
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071057-34593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071057-15200.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071058-39558.png)
∵f(x)的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071058-73801.png)
∴由
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071058-62160.png)
∴f(x)在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071058-77042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071059-64066.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071059-13346.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071059-51383.png)
(Ⅱ)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071059-91780.png)
①当a+1≤0,即a≤-1时,f′(x)<0∴f(x)在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071059-81428.png)
②当a≥0时,f′(x)>0∴f(x)在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071100-26687.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071100-25252.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071100-79915.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071100-62032.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071100-23926.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071101-22635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071101-46950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071101-82622.png)
综上,当a≥0时,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071101-57777.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071102-20885.png)
当-1<a<0时,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071102-71607.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071102-24339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071102-79076.png)
当a≤-1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071103-48391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071103-27431.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071048-10580.png)
(1)当a=b=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071048-41035.png)
(2)令F(x)=f(x)+
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071049-63984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071049-73273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071049-71022.png)
(3)当a=0,b=﹣1时,方程2mf(x)=x2有唯一实数解,求正数m的值.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071034-31930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071034-71043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071034-53833.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071034-80471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071035-38513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071035-39971.png)
(1)求函数y=f(x)在A(-1,f(-1)),B(2,f(2))两点处的切线的夹角的正切值;
(2)已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071035-85574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071035-39603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071025-64222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071025-24345.png)
(Ⅰ)求 x0和b 的值;
(Ⅱ)求证:在定义域内 f(x)≥0恒成立;
(Ⅲ) 若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071025-31592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071025-23788.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071019-95664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071020-45455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071020-42242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071016-37411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071016-14840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071016-44226.png)
B. 11万件
C. 9万件
D. 7万件
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