题目
题型:高考真题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055938-39074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055938-35328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055938-29913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055938-34989.png)
(Ⅰ)求集合
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055938-67696.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-35045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-28489.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-79452.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-19921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-84144.png)
所以可分以下三种情况:
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-64827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-69366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055939-45251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055940-54934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055940-56762.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055940-96195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055940-58548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055940-72952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055940-71998.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055941-24598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055941-33439.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055941-90362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055941-45133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055941-29230.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055942-97594.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055942-30504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055942-91892.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055942-22464.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055942-71586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055943-56049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055943-87735.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055943-10661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055943-81378.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055943-17649.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055943-35651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055944-49074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055944-42694.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055944-54140.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055944-28527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055944-52615.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055945-38285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055945-83354.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055945-21982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055945-73536.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055945-38289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055945-68745.png)
其中
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055946-69732.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055946-86837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055946-41697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055946-41730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055946-11436.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055947-65136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055947-32093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055947-46569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055947-84367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055948-29687.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055948-67074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055948-76260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055948-42152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055948-38660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055949-32310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055949-29887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055949-39322.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055949-13688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055950-37537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055950-64973.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055950-52763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055950-70231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055950-19114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055951-71290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055951-22847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055951-47399.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055951-54645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055952-34829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055952-20936.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055952-82934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055952-93574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055952-80669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055953-69772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055953-35272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055953-22399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055953-71208.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055954-90409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055954-44493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055954-17778.png)
④当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055954-74776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055954-64180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055955-74853.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055955-51037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055955-96333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055955-13514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055956-73347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055956-26220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055956-42836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055956-77036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055956-53757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055957-97810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055957-29799.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055957-23989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055957-16924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055957-91090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055958-36836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055958-54324.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055919-44451.png)
(Ⅰ)讨论
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055919-34678.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055919-90040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055919-84300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055919-34286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055919-43110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055920-74638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055920-74871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055920-95627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055920-75892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055915-16050.png)
B.函数f(x)有极大值f(-2)和极小值f(1)
C.函数f(x)有极大值f(2)和极小值f(-2)
D.函数f(x)有极大值f(-2)和极小值f(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055910-30534.png)
(1)求a的值;
(2)求函数f(x)的极值。
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019055904-71941.png)
(Ⅰ)设{an}是正数组成的数列,前n项和为Sn,其中a1=3.若点(an,an+12﹣2an+1)
(n∈N*)在函数y=f′(x)的图象上,求证:点(n,Sn)也在y=f′(x)的图象上;
(Ⅱ)求函数f(x)在区间(a﹣1,A)内的极值.
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