1 . 已知函数
.
(1)设函数
,若曲线
在点
处的切线方程为
,求
的值;
(2)是否存在实数
,使得
对
恒成立?若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81344623eb224cd50013c7ba7844bfa8.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4f764b0d11755922ef4f6c55297248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80cf0f8829ad6ed064ba129545b2d3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c14e7a0c4dce57fd2b86eba638692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8748f9bf0e49e067f65b9ce54c4718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)求函数
的单调区间和极值;
(2)是否存在实数
,使得函数
在
上的最小值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87ddae11c4ba01e12bcaf3419a22e2f.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579e2c39e6c0a640357e3b0ccd6f954a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-08-13更新
|
432次组卷
|
5卷引用:河北省邢台市2016-2017学年高二下学期期末考试数学(文)试题
河北省邢台市2016-2017学年高二下学期期末考试数学(文)试题(已下线)专题3.3 导数与函数的极值、最值-2021年高考数学(理)一轮复习-题型全归纳与高效训练突破(已下线)专题3.3 导数与函数的极值、最值-2021年高考数学(文)一轮复习-题型全归纳与高效训练突破安徽省滁州市定远县重点中学2020-2021学年高三上学期1月质量检测数学(理)试题山东省济宁市育才中学2022-2023学年高三上学期开学数学试题
名校
解题方法
3 . 已知函数
.
(1)当
时,求证:
;
(2)当
且
时,求函数
的最小值;
(3)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ce71a6ca213658ff3021dfac2381f.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/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab43bfe3e5c8547c2ea6cebfb38bbf0e.png)
您最近一年使用:0次
4 . 已知函数
,
.
(1)设
,
,求证:对任意正数
,在
与
中至少有一个不大于0;
(2)讨论函数
在区间
上零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d98d202ef9a558a0eddd880b8c61956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b9b1c88fbd3763062c7235b0ad39111.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d32785abcc3f7ffa3c4d1b06f5bc4c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5389fc8b0b381254b10f510838f0af7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065a4a241c5f9e6c1a84fc4705d9b267.png)
您最近一年使用:0次
解题方法
5 . 若函数
满足:
,
,其中
为
的导函数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e81c17b07aac0d43ec0ed6705b6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c335c8f0f025916707d16fc51f0d3278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a53de2e60c85b2044ed87efc5b76b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 已知函数
.
(1)若
对
恒成立,求实数
的取值范围;
(2)是否存在整数
,使得函数
在区间
上存在极小值,若存在,求出所有整数
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8dd4f27a6db537f221cd1db1ce8caf.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c4e7f9b9ec6207cc8a7230b663303a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)是否存在整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fec6b10af2705e7482249295c30161a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2017-02-16更新
|
1215次组卷
|
3卷引用:2016-2017学年河北省邢台市第一中学高二下学期第二次月考数学(理)试卷
名校
7 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2931eea90af73f958475cfe5115289.png)
(1)求
的单调区间;
(2)证明:曲线
不存在经过原点的切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2931eea90af73f958475cfe5115289.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
您最近一年使用:0次
2016-12-04更新
|
1048次组卷
|
4卷引用:2016-2017学年河北省邢台市第一中学高二下学期第二次月考数学(理)试卷
8 . 已知函数
.
(Ⅰ)求函数
的单调减区间;
(Ⅱ)记函数
的图象为曲线
.设点
是曲线
上的不同两点.如果在曲线
上存在点
,使得:①
;②曲线
在点
处的切线平行于直线
,则称函数
存在“中值和谐切线”.当
时,函数
是否存在“中值和谐切线”,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ead297722965b0b8509523ed3bd8adc.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4daf40bad1cc89311930cce356672354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c45b5bbd5fb7706c6f7c24df34fc145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
9 . 设
.
(1)如果
在
处取得最小值
,求
的解析式;
(2)如果
,
的单调递减区间的长度是正整数,试求
和
的值.( 注:区间
的长度为
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a6040b7af3d749da8cbd4ed5111ef0.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eca1ac021acc216e9fb38816c2ad6d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a955ba5c572b82d3695c86833c82ce11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b0a86d43e0a7f5f6719b2b7a153424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce421674556f3479ffca372cbc93b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d4cd90a9671c1b4589a34d3538ff12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65bb83b1daf4c79e6a10ec01a466425.png)
您最近一年使用:0次
2016-12-04更新
|
218次组卷
|
2卷引用:河北省巨鹿中学2016-2017学年高二下学期第三次月考数学(理)试题
10 . 若以曲线
上任意一点
为切点作切线
,曲线上总存在异于
的点
,以点
为切点作切线
,且
,则称曲线
具有“可平行性”.下列曲线具有可平行性的编号为________ .(写出所有满足条件的函数的编号)①
②
③
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f333597681f659970192b179a2ed4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f59fc26170738dcf2fabe884a77953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0660d4864c16652a6b27337462b3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc877e18ddca2a1a06a9b74fd6b6c588.png)
您最近一年使用:0次