真题
解题方法
1 . 已知函数
,
.
(1)证明:当
时,
在
上是增函数;
(2)对于给定的闭区间
,试说明存在实数k,当
时,
在闭区间
上是减函数;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3c267c46b3e503a97cf11a08cd5cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dc3a93128cc0bbf6d36e42e2eff454.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f19bb8718ccb46af2fe8aa22759d69a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)对于给定的闭区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4318dc1a6f86b65714ac6b762de0a4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a3275978bc2d7766a62f96ae4fdccbe.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)当
时,试比较
与
的大小;
(2)若斜率为
的直线与
的图象交于不同两点
,
,线段
的中点的横坐标为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c64d70d50cb38406a508aeb1837e11.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb19d43bf321e4019573260f189a7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63d7758a927384c13052ae432c20a23.png)
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a193c4c10cbbf7d3a6eca993f8abb5.png)
您最近一年使用:0次
3 . 已知函数
.
(1)若
,求
的极值;
(2)若
是
的两个零点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec94a777e5f62833727151ea6bb21424.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19a80063c7bcb52362a94bf389e1b99.png)
您最近一年使用:0次
2023-03-11更新
|
1178次组卷
|
8卷引用:辽宁省锦州市黑山县黑山中学2023届高三一模数学试题
解题方法
4 . 已知函数
.
(1)若
在
上恒成立,求实数a的值;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762b3bb4b9b16cfe24bc6424fb3d2483.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4eb10694a54696e4295d1887d27005.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e8f6ccc68df1a4d8bb5b7d2a82fc4f.png)
您最近一年使用:0次
2023-01-18更新
|
691次组卷
|
5卷引用:辽宁省2022-2023学年高三上学期期末联考数学试题
辽宁省2022-2023学年高三上学期期末联考数学试题辽宁省朝阳市2023届高三上学期期末数学试题(已下线)导数与不等式(已下线)第六章 导数及其应用(A卷·知识通关练)(5)(已下线)拓展五:利用导数证明不等式的9种方法总结-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)
名校
5 . 已知函数
.
(1)若
,判断函数
有几个零点,并证明;
(2)若
不是函数
的极值点,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6025607ec4c367dee2f1b70a24f3415d.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/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68072473a5106f93e3026d992859f7a1.png)
您最近一年使用:0次
6 . 已知函数
.
(1)判断函数
在区间
上零点和极值点的个数,并给出证明;
(2)若
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f448e220769c620ed39ad87a802fa00.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f42af9fa3a5ce80dafd4ab8e8ef0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
7 . 已知函数
,其中
.
(1)若
,讨论函数
的单调性;
(2)已知
,
是函数
的两个零点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86187410f634d2f68704b05d9ee49d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6a8b94c02716736000e2e817b532a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7825b129635e3c3c4aba6f17aa0007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684bcf84f0a266515bfafde0da903050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3c7bb85e44e9fdeb0a51875fb8804b.png)
您最近一年使用:0次
2023-07-18更新
|
479次组卷
|
4卷引用:辽宁省五校2022-2023学年高二下学期期末数学试题
名校
解题方法
8 . 已知函数
.
(1)当
时,若曲线
在
处的切线方程为
,证明:
;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f9d489bd3ee783ae33d5c059b19c5d.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/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3ce4451ce64e6385d8015c112e68b0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc119537024aa4c222ee3d26de0c0c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-01-15更新
|
1308次组卷
|
4卷引用:辽宁省大连市育明高级中学2023-2024学年高三上学期期中数学试题
辽宁省大连市育明高级中学2023-2024学年高三上学期期中数学试题四川省成都市2023届高三第一次诊断性检测数学(理科)试题(已下线)第五章 一元函数的导数及其应用 (单元测)(已下线)专题05函数与导数(解答题)
名校
解题方法
9 . 已知函数
(
).
(1)若函数
的极大值为0,求实数a的值;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4243cf6e83bacc036280eada841a6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1543a59401c671def4f045df9e5e0ca8.png)
您最近一年使用:0次
2023-02-06更新
|
446次组卷
|
3卷引用:辽宁省铁岭市昌图县第一高级中学2022-2023学年高二下学期6月月考数学试题
辽宁省铁岭市昌图县第一高级中学2022-2023学年高二下学期6月月考数学试题四川省攀枝花市2023届高三上学期第一次统一考试数学(理)试题(已下线)拓展五:利用导数证明不等式的9种方法总结-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)
名校
解题方法
10 . 已知函数
.
(1)求
在区间
内的极大值;
(2)令函数
,当
时,证明:
在区间
内有且仅有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56ec2258720b77cd82dc6510acc563b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)令函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1582c12e318db71ef25098e6f8872655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79e9bca78d1e27e7a72b6125c796f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
您最近一年使用:0次
2023-01-16更新
|
1252次组卷
|
3卷引用:辽宁省名校联盟2023届高考模拟调研卷数学(三)