名校
1 . 已知函数
.
(1)若
在点
处的切线与
轴平行,求
的值;
(2)当
时,求证:
;
(3)若函数
有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62748fb186797f6ec7b8e10f22c4d338.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0606c4ffcfe6f4709155d1e8671ee57.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-02-15更新
|
381次组卷
|
2卷引用:山东省日照市2021-2022学年高三上学期12月校际联合考试数学试题
解题方法
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3f95209a5660d863390796bdb757b3.png)
(1)求
的最小值;
(2)函数
的图象是一条连续不断的曲线,记该曲线与
轴围成图形的面积为
,证明:
;
(3)若
对于任意
恒成立,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3f95209a5660d863390796bdb757b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bfb294ca153bb081de0eb105540a8c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25b8875642519f32b09de7338dfa336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dff3ece45bf6c91d9dd8d07ae72584d.png)
您最近一年使用:0次
解题方法
3 . 已知函数
,
.
(1)当
时,若曲线
与直线
相切,求k的值;
(2)当
时,证明:
;
(3)若对任意
,不等式
恒成立,求a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)
(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/6e743e06a79e9796e0212ab8dcac3a9f.png)
您最近一年使用:0次
2022-11-11更新
|
625次组卷
|
4卷引用:山东省泰安市新泰市第一中学北校2022-2023学年高三上学期期中考试数学试题
名校
解题方法
4 . 已知函数
.
(1)若过原点的一条直线
与曲线
相切,求切点的横坐标;
(2)若
有两个零点
,且
,证明:
①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77fb3b218a67bd1fc2d1883f4fba546.png)
(1)若过原点的一条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6657f5dd2a7723fcee6a7a10ca21d2d4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16029d6e5e7c97938f581cf40cc32e2f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f929851b93fda5c6c29b9400397cdc.png)
您最近一年使用:0次
2022-10-11更新
|
1172次组卷
|
5卷引用:山东省潍坊市临朐县实验中学2022-2023学年高三10月月考数学试题(实验班)
解题方法
5 . 已知函数
.
(1)若曲线
在
处的切线经过点
,求实数a的值;
(2)若对任意
,都有
(e为自然对数的底),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db925e05c2fe79adca7fe09a77d4b67e.png)
(1)若曲线
![](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/7160d93f92089ef36f3dab809d3114b8.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061daa216e14972621d1a5748e5ddca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fe2115d883d13561e28006d3f6143b.png)
您最近一年使用:0次
2022-03-13更新
|
1840次组卷
|
6卷引用:山东省济宁市梁山现代高级中学2021-2022学年高二下学期3月月考数学试题
山东省济宁市梁山现代高级中学2021-2022学年高二下学期3月月考数学试题中学生标准学术能力诊断性测试2022届高三3月测试数学文科试题(已下线)专题5 隐零点问题(已下线)拓展八:导数隐零点问题的6种考法总结-【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)(已下线)第四章 导数与函数的零点 专题四 导数中隐零点问题 微点3 导数中隐零点问题(三)宁夏银川市永宁县上游高级中学2024届高三上学期月考(四)数学(理)试题
6 . 设函数
,
.
(1)若直线
是曲线
的一条切线,求
的值;
(2)证明:①当
时,
;
②
,
.(
是自然对数的底数,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0ec3c50f8ff3bbb30ba0a0962073f2.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87490be8d0cdb7bc6c39d1a37f3bc335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb31e419ea4e0ec8f06d8cb4e348debc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dacb2a0080a87354011933ee07008f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25da8298b6a96d627f3e8c990e55f0c.png)
您最近一年使用:0次
2022-09-19更新
|
1125次组卷
|
4卷引用:山东省烟台市招远市第二中学2022-2023学年高三上学期9月月考数学试题
名校
7 . 已知函数
.
(1)若曲线
在点
处的切线与x轴平行.
①求实数a的值:
②证明:函数
在
内只有唯一极值点;
(2)当
时,证明:对于区间
内的一切实数,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39e7afff8b484778ad556a10770fef6.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
①求实数a的值:
②证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a987feb9df03831a505b0015fc5536a6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5607726c179e749a99798bfd2318185b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7c4922d76ff755e83553365ad8c313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
您最近一年使用:0次
2022-09-09更新
|
645次组卷
|
3卷引用:山东省日照市日照第一中学2022-2023学年高三上学期10月月考数学试题
名校
解题方法
8 . 已知
,
为函数
的两个零点,
,曲线
在点
处的切线方程为
,其中
为自然对数的底数.
(1)当
时,比较
与
的大小;
(2)若
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b854f88a901132d2268d9690dfef2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5410c32fbf47d8f5b6512c2f9b66df0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1f08e04cf0b6a9afea66ce590ba00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0cc202753558c28d925d782b27198a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58d17d46045f9cd1f85a3c4f2ff912f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34074712b8e0c787f0a1cfd4133ee46.png)
您最近一年使用:0次
2022-05-31更新
|
1148次组卷
|
2卷引用:山东省淄博市2022届高三三模数学试题
解题方法
9 . 已知函数
的图象在
点处的切线为.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78b2837242e54d8d92cf1fe64938f66.png)
(1)求
;
(2)求证:
;
(3)已知
,若
对
恒成立,求正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08caec54ff2cc4a3fff76c40cb1bfc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78b2837242e54d8d92cf1fe64938f66.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b2562dee02aad3f4d5c87f404ac1e0.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55748bb2092b8c0427433a61c5c54e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6568ec3c84d8a01ef4204fe88ff9d17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/739acb356dcabf29bce2e406c604d322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-01-23更新
|
571次组卷
|
3卷引用:山东省青岛市四区2021-2022学年高三上学期期末考试数学试题
10 . 已知函数
.
(1)求曲线y=f(x)在x=1处的切线方程;
(2)证明:f(x)≥1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0611242edfea777f165bb37048e9f1c8.png)
(1)求曲线y=f(x)在x=1处的切线方程;
(2)证明:f(x)≥1.
您最近一年使用:0次