名校
解题方法
1 . 已知函数
.
(1)若当
时,
,求实数
的取值范围;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1a7af736682fe8e230b383f930a609.png)
(1)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3368388525e30cb7179909b03184eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a6e50a5235445f37996724ebdba0f1.png)
您最近一年使用:0次
2024-01-31更新
|
800次组卷
|
3卷引用:山西省晋中市、大同市2024届高三上学期适应性调研联合测试数学试题
山西省晋中市、大同市2024届高三上学期适应性调研联合测试数学试题江苏省南京师范大学附属中学2023-2024学年高三上学期期末模拟数学试题(已下线)重难点2-4 利用导数研究不等式与极值点偏移(8题型+满分技巧+限时检测)
解题方法
2 . 已知函数
,
.
(1)求证:函数
存在单调递减区间,并求出该函数单调递减区间
的长度
的取值范围;
(2)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43d3391304d235789fb72d6e21f2e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92231ba0e780c53511c9c386b60ec6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)证明:
有唯一的极值点;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4234a8028f8f2b502c31ef8ff9d0ad.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-12-29更新
|
578次组卷
|
5卷引用:山西省朔州市怀仁市2023-2024学年高三上学期第二次教学质量调研数学试题
名校
解题方法
4 . 已知
.
(1)若
,求
的极值;
(2)若
,
,
,且
,其中
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e122c7329920b109dfc31a515f8ce9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56e950ab080935c87103ae58973b1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8bb88c7df826a773c3013e32d07adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b809246e1ba4e9f8cb251cffde332e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5a523e020e21797c0f83c2b6772588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9a9a57f5c1318e2d3cb29d8abf5c09.png)
您最近一年使用:0次
2023-07-04更新
|
350次组卷
|
2卷引用:山西省大同市浑源中学2022-2023学年高二下学期期末数学试题
名校
5 . 已知函数
,
,
.
(1)当
时,证明:
时,
恒成立;
(2)若
在
处的切线与
垂直,求函数
在区间
上的值域;
(3)若方程
有两个不同的根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a42c6456bf9804a5af9a3047839d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefcdb01d4faefe432560366455f7fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7df077f5f5d14605b14f6d7620564ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9741af1fd8e651860c2fcf2c6846347.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89eea593c79973e97f6f3cdf621cdfc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79f305c99f334478d00e6e582215ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec89d17a1b8f7961e2f1f27c2d50685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89eea593c79973e97f6f3cdf621cdfc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7df664d2387537018c7b877ea08ef2.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7967adb601d3a654644279adaab4521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-18更新
|
249次组卷
|
2卷引用:山西省大同市阳高县第四中学校2022-2023学年高二下学期期末数学试题
名校
解题方法
6 . 已知函数
.
(1)求
的最大值;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b607ae39876e8d35bf2e6576ff4ee96f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5d54ea50d01535318b10a9fa570931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe15555c21773fbd8028f48d250054a.png)
您最近一年使用:0次
2023-04-26更新
|
502次组卷
|
2卷引用:山西省阳泉市第一中学2021-2022学年高二下学期期末数学试题
解题方法
7 . 已知
.
(1)当
,证明
;
(2)讨论
的单调性;
(3)利用(1)中的结论,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebc745a5447d68aa4d43aaff2614a42.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)利用(1)中的结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450940c16da05563afa896f50ac33332.png)
您最近一年使用:0次
解题方法
8 . (B)已知函数
.
(1)讨论函数
在
上的单调性;
(2)若
有两个极值点
,且
,求证:
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b46c734f7c5ad829b17b0928c2e08.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad346f74f037ab200b0c4ad34610e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6657f5dd2a7723fcee6a7a10ca21d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3fe8ad699c43bc6a456367aa2a8d2e.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59004c5916a745f186e0bd66aa3bca2.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
.
(1)当
时,求
的极值;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4edb7a02925b48bfed6dc873bcb7237.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61206c100106c922b4cc65a5197f0f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d8844a1a5ba858f68e4124cef4bbdd.png)
您最近一年使用:0次
2022-12-19更新
|
400次组卷
|
3卷引用:山西省忻州市2021-2022学年高二下学期期末联合考试数学试题
山西省忻州市2021-2022学年高二下学期期末联合考试数学试题河北省文安县第一中学2021-2022学年高二下学期期末数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21
解题方法
10 . 已知
.
(1)求证:
恒成立;
(2)令
,讨论
在
上的极值点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6064ea5c9236e2ccbd91de0368c67a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ba34ec42d35224b021c44eecacbcb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1e76aaf12e83bd85df89b42ab2eef5.png)
您最近一年使用:0次
2023-01-10更新
|
375次组卷
|
2卷引用:山西省吕梁市2023届高三上学期期末数学试题