解题方法
1 . 已知函数
.
(1)讨论
的单调性;
(2)若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f2247b4830f0984819e43822722447.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6472cc029d5a2578c992feef08326e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 对于函数
,若实数
满足
,则
称为
的不动点.已知函数
.
(1)当
时,求证:
;
(2)当
时,求函数
的不动点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283794ec542a53ccc16cf5fcb1367bec.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)当
时,证明:
有且仅有一个零点.
(2)当
时,
恒成立,求a的取值范围.
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467fb8a741acbbae9548afdc186cd686.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f6313f09d17496008ebe3cc1fca0ca.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade0e43ca66880fa7a94c2121bfd0df2.png)
您最近一年使用:0次
2024-04-23更新
|
989次组卷
|
4卷引用:内蒙古自治区呼伦贝尔市2024届高三下学期二模理科数学试题
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1506574b66c9944a2e281ad7635c7c.png)
(1)求函数
的单调区间;
(2)令
,求
在
处的切线
的方程,并证明
的图象在直线
的上方.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1506574b66c9944a2e281ad7635c7c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448757d2108dc92548c97728c7b59283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求函数
的单调递增区间;
(3)若函数
在区间
上只有一个极值点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec41bd3e8817a23ae44061c7b7380cf.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
2024-04-01更新
|
973次组卷
|
2卷引用:内蒙古赤峰市2024届高三下学期3·20模拟考试理科数学试题
6 . 已知函数
.
(1)若
是函数
的极值点,求a的值;
(2)求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ccd55ca132df0e4f09ed033a0510c7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
2024-03-27更新
|
1862次组卷
|
5卷引用:2024届内蒙古自治区包头市高三下学期二模文科数学试题
7 . 设函数
.
(1)当
时,讨论
的单调性,并证明
;
(2)证明:①当
时,
;
②当
时,
,当
时,
;
③当
时,函数
存在唯一的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/583f8821e1f933b3ae9ec56f82b20f60.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0852d49275f8774ba92620d8af490c72.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a16e7c0a12d8b0be5194fc875a19065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221d0bf6c8cf0a1ff429f556a4d9cd5f.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51e2b8f615b2cc7eca7fda25efb507d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
8 . 设函数
.
(1)当
时,讨论
的单调性;
(2)证明:①当
时,
;
②当
时,
,当
时,
;
③当
时,函数
在
单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968cc5646cb96896153bb60887d2c5f1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0852d49275f8774ba92620d8af490c72.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a16e7c0a12d8b0be5194fc875a19065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221d0bf6c8cf0a1ff429f556a4d9cd5f.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51e2b8f615b2cc7eca7fda25efb507d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
您最近一年使用:0次
9 . 已知函数
.
(1)判断函数
的单调性
(2)证明:①当
时,
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d419cdc9c5f81d7516022c872bc607a.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd69418358ad4e64c9e9ad2cfa429d5.png)
您最近一年使用:0次
2024-03-26更新
|
1122次组卷
|
4卷引用:内蒙古呼伦贝尔市2024届高三下学期一模数学(理)试题
内蒙古呼伦贝尔市2024届高三下学期一模数学(理)试题广东省广州四中2023-2024学年高二下学期期中数学试题(已下线)专题1 数列不等式 与导数结合 练(经典好题母题)(已下线)压轴题01集合新定义、函数与导数13题型汇总 -1
10 . 已知函数
.
(1)求
在
处的切线方程
,并证明
的图象在直线
的上方;
(2)若
有两个不相等的实数根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4b35e41dfa9391bf5004948d4ed574.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b331497342e72895c306815d1cca62b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b222b256b37f83fa24a3a4b6527f58d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5dc5d64a9a86dd15c47e7d129fc622.png)
您最近一年使用:0次