名校
解题方法
1 . 已知函数
,
,且曲线
和
在原点处有相同的切线.
(1)求实数a的值:
(2)证明:当
时,
;
(3)令
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82677d95bc109795e16401461dc6467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591d032abe536b6bfc4e04104dc921bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)求实数a的值:
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e96e2ed7d9cd25c06f9a51a7210a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d3ac6f2ecceac9566cdc98752ba2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343143dd8a6ce47f1ea1a32478a8a49e.png)
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2023-10-24更新
|
384次组卷
|
2卷引用:黑龙江省大庆市大庆实验中学2021年高三上学期10月月考数学试题
名校
2 . 已知函数
,
(1)当
时,求函数
在
处的切线方程;
(2)讨论函数
的单调性;
(3)当函数
有两个极值点
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5facb7583ea00e6d8db952d80557f4b.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b314f6ccb0a3e4fc15685d85e55bf6.png)
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2023-09-05更新
|
654次组卷
|
14卷引用:福建省宁化第一中学2022届高三9月第二次月考数学试题
福建省宁化第一中学2022届高三9月第二次月考数学试题广东省梅州市东山中学2022届高三上学期期中数学试题天津市第五十五中学2021-2022学年高三上学期10月学情调研数学试题云南衡水实验中学2022届高三上学期期中考试数学(理)试题黑龙江省哈尔滨工业大学附属中学校2021-2022学年高二上学期期末考试数学(理)试题(已下线)2020年高考天津数学高考真题变式题16-20题(已下线)第13讲 双变量问题-2022年新高考数学二轮专题突破精练河南省洛阳市洛宁县第一高级中学2022-2023学年高二下学期2月月考数学理科试题江苏省南京大学附属中学2022-2023学年高二下学期3月月考数学试题广西壮族自治区梧州市苍梧中学2022-2023学年高二下学期3月月考数学试题天津市五区县重点校2022-2023学年高二下学期期中联考数学试题(已下线)模块五 专题5 期中重组卷(广东)天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷2(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
3 . 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)
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2022-01-23更新
|
571次组卷
|
3卷引用:山东省青岛市4区县2021-2022学年高三上学期期末考试数学试题
4 . 已知函数f(x)=ax+lnx+1(a∈R),
.
(1)若y=g(x)的图象在x=0处的切线l与y=f(x)的图象相切,求实数a的值;
(2)若不等式f(x)≤g(x)对任意的x∈(0,+∞)恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cc2a47354e79ff4fefa6969816484b.png)
(1)若y=g(x)的图象在x=0处的切线l与y=f(x)的图象相切,求实数a的值;
(2)若不等式f(x)≤g(x)对任意的x∈(0,+∞)恒成立,求实数a的取值范围.
您最近一年使用:0次
名校
5 . 函数
.
(1)若a=1,求y=f(x)在点(1,f(1))处的切线方程;
(2)若
恒成立,求a的值;
(3)若
有两个不相等的实数解
,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93a4f5b20d30169bd85e5c82cf50da0.png)
(1)若a=1,求y=f(x)在点(1,f(1))处的切线方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ca4c9087d7b6603737d6354a4bf936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f8062ae945803fa02f0fac5c4ba2f9.png)
您最近一年使用:0次
6 . 已知函数
.
(1)若
,求曲线
在点(1,f(1))处的切线方程;
(2)若关于x的不等式
在
上恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c112d0f2cf768e34cf05b6b4740f9ae6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b053fcfbdb442f5e40dbff4408b94fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac07a11e274063879a45aafc9b9f320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
您最近一年使用:0次
名校
解题方法
7 . 设函数
,曲线
在
处的切线方程为y=-x+1.
(1)求实数a的值;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79eaff7eed6db183855181c5b7526536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求实数a的值;
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd0c7f779e914339655ed91ac2d5cbe.png)
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8 . 已知函数
.
(1)若直线l过点
,并且与曲线
相切,求直线l的方程;
(2)设函数
在
上有且只有一个零点,其中
,e为自然对数的底数,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3b6c56aee4bb8a8131fd960415c745.png)
(1)若直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ed712c13740c2c456f0668e3f931ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e734b17201fe992be7775714e9558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
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2022-02-13更新
|
587次组卷
|
2卷引用:四川省成都市石室中学2021-2022学年高三上学期专家联测卷(二)数学(理)试题
解题方法
9 . 已知函数
与
.
(1)若
与
在
处有相同的切线,求
、
,并证明
.
(2)若对
,都
使
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677fb21d94436bc9e92f3ef1ba22737f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03dd7b797412c4ac0d884a9781de7dec.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191e3c845e90f229f3c992aff85b92db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeec6bfdf6825e4a468ddc4158ab6398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021高二·江苏·专题练习
解题方法
10 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ff229e8416c2ff6e7208771acbf9b6.png)
(1)不等式
对于任意的
恒成立,求实数a的取值集合;
(2)若函数
与函数
的图象有且仅有一条公切线,求实数a的取值集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(3)设
,
,若函数
有两个极值点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10859140f06705b580f3ac3807e58d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ff229e8416c2ff6e7208771acbf9b6.png)
(1)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae4b12d8a282854010fdec8e2ec106d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d9c89d2cd1fb46b1e71ad10227c098.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5946299ed8f8c741a82c8d920e1e206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1163dc4158acac142a1d670eeab8ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ba925278baa53ad23a953fe62f2e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b479d1beea3cd559d9225da950a76eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760effa3c34aefb5d6bbd0e7ca0d48fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6fe150b0a721696c8c063999ba38d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae59a693d0d39d7afacbed93eb0abe9.png)
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