题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-36109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-39015.png)
⑴当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-85965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
⑵求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
⑶证明对任意的正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-61195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-40565.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-85965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-56566.png)
⑵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-43334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-43113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-27272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-44289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-80494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-50405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
⑶证明见解析
解析
(1)先求解函数的定义域,然后求解导数,令导数大于零或者小于零得到单调区间。
(2)由⑴得当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-85965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-75621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-70116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-49759.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-41865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-57107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-31308.png)
函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-29974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-16532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-68824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-47625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-88228.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-92908.png)
解:⑴由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-56566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-68687.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-33796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-64010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-36343.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-85965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-31688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-25382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-56566.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-62452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-60703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-11347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-62452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-85965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-56566.png)
⑵①由⑴得当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-85965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112259-41576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112259-21899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112259-41913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112259-88143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-11347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112259-55234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-11347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112258-62452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112259-41576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-56566.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-75027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-15415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-89523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-55521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-55821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-65145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-25638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112301-95580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112300-55821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112301-97011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112301-72745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112301-26888.jpg)
由此表可知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-43334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112302-26985.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-27272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112302-79278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112302-85713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112301-97011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112301-72745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112302-64610.jpg)
由此表可知:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112302-67506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112303-78621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112303-33298.png)
综上所述:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-43334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-43113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-27272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-44289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112254-80494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-50405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112250-79124.png)
⑶当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-75621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-70116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-49759.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-41865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112255-57107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-31308.png)
函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-29974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-16532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-68824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112256-47625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-88228.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112257-92908.png)
故当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112303-91303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112303-42632.png)
对任意正整数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-61195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112304-59641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112253-40565.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-89963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-72882.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-54841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-29048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-25415.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-37545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-92460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112238-29315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112221-25212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112221-19702.png)
(1)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112221-51957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112221-66852.png)
①求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112221-32846.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112222-92749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112221-32846.png)
(2)若存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112222-63821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112222-18478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112222-78360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112223-74784.png)
①f(x)>0的解集是{x|0<x<2};
②f(-)是极小值,f()是极大值;
③f(x)没有最小值,也没有最大值.
A.①③ | B.①② | C.② | D.①②③ |
A.( -1 ,0 ) | B.( -1 ,+![]() | C.(0 ,+ ![]() | D.(1 ,+ ![]() |
求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018112159-32663.png)
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