名校
解题方法
1 . 已知函数
.
(1)若
,求函数
的图象在
处的切线方程;
(2)若
对任意的
恒成立,求a的取值范围;
(3)求证:
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ae6426dabbe4bc05cd634b782900b3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797ddd319a706b744f44b476bdeb9feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
您最近一年使用:0次
2023-11-27更新
|
663次组卷
|
6卷引用:青海省西宁市大通县2024届高三第二次模拟考试数学(理)试题
青海省西宁市大通县2024届高三第二次模拟考试数学(理)试题四川省2024届高三上学期第四次联考(月考)理科数学试题湖南省长沙市长郡中学2023-2024学年高二上学期阶段性检测数学试卷河北省保定市唐县第一中学2023-2024学年高二上学期阶段性检测数学试题山东省菏泽市鄄城县第一中学2024届高三上学期1月月考数学试题(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)
解题方法
2 . 已知函数
.
(1)若
,求函数
的最大值;
(2)若
恒成立,求
的值;
(3)令
,过点
作曲线
的两条切线,若两切点横坐标互为倒数,求证:点
一定在第一象限内.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d71b8255ff798aa65c960ad7fe43238.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3c601836429e5d2f583b0ea4f02780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17553730682405c04b962f66ce5fd92d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5a90aeba435af22d6bcdb7b91650b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
.
(1)若
在
上单调递增,求a的取值范围,
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32eb62105d3c9113c9c4715e404825fc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324c5822114cf4bf2063fb2ddaa27e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
您最近一年使用:0次
2023-03-22更新
|
1102次组卷
|
5卷引用:青海省西宁市大通回族土族自治县2023届高三第二次模拟考试文科数学试题
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25ab4f80679d9ee97529f7bd3dd4c29.png)
(1)若
,证明:
存在唯一极值点.
(2)若
,证明:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25ab4f80679d9ee97529f7bd3dd4c29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d30e582553a6e95f13fd7ddb571f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddc641f2dfa5191b020bb82253934f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
您最近一年使用:0次
2022-12-21更新
|
296次组卷
|
4卷引用:青海省西宁市大通回族土族自治县2023届高三一模数学(文)试题
5 . 已知函数
.
(1)若
,证明:
存在唯一的极值点.
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655d325b121553372ee0fee9c4eb61e2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a323813f130b8311fc70574a2cdd8a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-12-21更新
|
330次组卷
|
4卷引用:青海省西宁市大通回族土族自治县2023届高三一模数学(理)试题
名校
解题方法
6 . 已知函数
,
.
(1)当
时,若曲线
与直线
相切于点
,求点
的坐标;
(2)当
时,证明:
;
(3)若对任意
,不等式
恒成立,求出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be838347582147fe01c6a1338a889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8e8b6b50410876780b97fd192e8829.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5af632ae8a9eedbbd77ac6bf9615d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-09-03更新
|
1013次组卷
|
6卷引用:青海省西宁市七校2021-2022学年高二下学期期末联考数学(文)试题
青海省西宁市七校2021-2022学年高二下学期期末联考数学(文)试题北京大学附属中学2022届高三三模数学试题北京市第二十二中学2023届高三上学期开学考试数学试题(已下线)专题09 导数及其应用难点突破1(已下线)专题12 导数及其应用难点突破4-利用导数解决恒成立问题-2(已下线)第5章 导数及其应用(基础、常考、易错、压轴)分类专项训练(原卷版)
名校
解题方法
7 . 已知函数
,
.
(1)若
,证明:
;
(2)若
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e302bb552f3b17d4428b7c48629ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495b767764be7fd47876dcebb6f51970.png)
您最近一年使用:0次
2022-06-20更新
|
665次组卷
|
2卷引用:青海省2022届高三五月大联考理科数学试题
名校
解题方法
8 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,证明:
.(注
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbc1e68e60a02d990d846b4303d551b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b717e559b68f93be0fa22d4275b09aa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52881be613aa404e553da30d8987cfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
您最近一年使用:0次
2022-06-10更新
|
462次组卷
|
3卷引用:青海省玉树州州直高中2021-2022学年高三下学期第四次大联考数学(理科)试题
解题方法
9 . 已知函数
,曲线
在
处的切线与直线
垂直.
(1)求
的值.
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d95aa7445ae32ebce0f7aa3a284327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f129d441ab39d195cb2580c46065d0fb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac0c4f74d16d30a8799b03b41460cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c62b3c44e262862c5d29c0d28ae17c6.png)
您最近一年使用:0次
2022-05-10更新
|
592次组卷
|
2卷引用:青海省西宁市大通回族土族自治县2022届高三第二次模拟考试数学(理科)试题
名校
10 . 已知函数
.
(1)若
,证明:
;
(2)讨论
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92cb70ebc1443289114cac655ec2a55.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次