解题方法
1 . 已知函数
(
为非零常数),记
,
.
(1)当
时,
恒成立,求实数
的最大值;
(2)当
时,设
,对任意的
,当
时,
取得最小值,证明:
且所有点
在一条定直线上;
(3)若函数
,
,
都存在极小值,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4187aadeb68df93870c9e416ad7244c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7708ba23f01d33c69df8ea236c876f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b8ae9ec829851d83bfb73429ee8009.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe24ccc3dd4dbadd2f757cf7b7a44a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b43f4c5b17fb428231e2958c36404b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4836fe2c858dbfaa6baeaf7e50a24cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9acaba1f9b687c7cdd4cf9924f19047f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d413c25f6271c3b97a668dc47b8d7de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104b081cfbc9120b476831c79a749c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548636534994cd465dfc7bf7dd41505b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 已知函数
,其中a,b为常数,
为自然对数底数,
.
(1)当
时,若函数
,求实数b的取值范围;
(2)当
时,若函数
有两个极值点
,
,现有如下三个命题:
①
;②
;③
;
请从①②③中任选一个进行证明.
(注:如果选择多个条件分别解答,按第一个解答计分)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6580d916c40fe9f37b3b5cdda767780c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e373fa26b51a4c2060be2345be00761c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c013dd461282a9677073747d55f685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb7c63c22dc5e9ae9b17a693af2424c.png)
请从①②③中任选一个进行证明.
(注:如果选择多个条件分别解答,按第一个解答计分)
您最近一年使用:0次
名校
3 . 设函数
.
(1)当
时,
的最小值为5,求
的值:
(2)当
时,设
是函数
图象上的两个动点,且在A,B处的两切线
互相平行,求证:直线AB必过定点,并求出此定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57363b27165d20f8aca704f33e5bb0b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538193a4717d564c01145e82314c2d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed535fdab3babeaf6447edaafbccc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
您最近一年使用:0次