解题方法
1 . 设函数
.
(1)若关于
的不等式
在
为自然对数的底数)上有实数解,求实数
的取值范围;
(2)设
,若关于
的方程
至少有一个解,求
的最小值;
(3)证明不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b407e8ad76ad0e64896bfb51ef054d.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6cf5ba23618b68a2fe6fe0fc45520d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42016a34f6f615c939e95e4ec8de1b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb61c150a07b4058b8417cf7bb6027a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b43db2ccdd3c135d96886302b0765d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4cd85fe5cb85a16a6b6293b40ac9fa2.png)
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解题方法
2 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3473c109ec4d71f833dad76eb5d145.png)
(1)若关于
的不等式
在
有实数解,求实数
的取值范围;
(2)设
,若关于
的方程
至少有一个解,求
的最小值.
(3)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3473c109ec4d71f833dad76eb5d145.png)
(1)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfcbc3ffca28dadd8241999c35cb49c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91e6d30e5e96f240b538c55aa1da9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed0a706f0f99690a25194a4586cea66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790b807c406d6f22dc559b1ec16f9356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/688955342aa1c114d7fcc04618974410.png)
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名校
3 . 已知函数
.
(1)当
时:
①解关于
的不等式
;
②证明:
;
(2)若函数
恰有三个不同的零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca766a161f9438aef446b1beb7de3c4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
①解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d80a96345f600468f0efb316ccd586.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1048afd2ea59732a2119a2863ed77b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-01-11更新
|
1236次组卷
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4卷引用:中学生标准学术能力诊断性测试2021-2022学年高三上学期1月月考数学试题
名校
4 . 已知函数
,
,其中
.
(1)若方程
在
(
为自然对数的底数)上存在唯一实数解,求实数
的取值范围;
(2)若在
上存在一点
,使得关于
的不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b25cf08bf05e3f4ccd2e4d535c69ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95a3d7b6e442c071058580d95f9e239c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3a6b1966bfca879c8de2e46048eb24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-07-29更新
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3卷引用:开卷教育联盟2020届全国高三模拟考试(四)数学理科试题
名校
5 . 函数
.
(1)求
的单调区间;
(2)若
只有一个解,则当
时,求使
成立的最大整数k.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61edbe77befb7e5354100d04b603d9c1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f2c3547f47ce4f1ddcd38dc180175d.png)
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7日内更新
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3卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题
山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题河北省邯郸市部分示范性高中2024届高三下学期三模数学试题(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
6 . 已知函数
,且
.
(1)讨论
的单调性;
(2)若方程
有三个不同的实数解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38c7516e436ac50944c7e458512f889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28b08682efa2692b052f64fe1448fce.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d728ffe921d0a87b909fd266243a09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
7 . 对于三次函数
.定义:①
的导数为
,
的导数为
,若方程
有实数解
,则称点
为函数
的“拐点”;②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
恒成立,则函数
的图象关于点
对称.
(1)已知
,求函数
的“拐点”
的坐标;
(2)检验(1)中的函数
的图象是否关于“拐点”
对称;
(3)对于任意的三次函数
写出一个有关“拐点”的结论(不必证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](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/5abde3621d19a60d8b0cad42c06d8891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5f97843013ef486e10f66543562a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)对于任意的三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
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8 . 对于三次函数
.定义:①
的导数为
,
的导数为
,若方程
有实数解
,则称点
为函数
的“拐点”;②设
为常数,若定义在
上的函数
对于定义域内的一切实数
,都有
恒成立,则函数
的图象关于点
对称.
(1)已知
,求函数
的“拐点”
的坐标;
(2)检验(1)中的函数
的图象是否关于“拐点”
对称.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1fa6ca9eb7cea9131dad36db6a0ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](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/5abde3621d19a60d8b0cad42c06d8891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5f97843013ef486e10f66543562a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)检验(1)中的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
9 . 设
.
(1)讨论
的单调性;
(2)若对任意的
,关于
的方程
有两个不相等的实数解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d868044b1b26bdba1c449f80794dcd3a.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
10 . 给出定义:设
是函数
的导函数,
是函数
的导函数,若方程
有实数解
,则称
)为函数
的“拐点”.
(1)经研究发现所有的三次函数
都有“拐点”,且该“拐点”也是函数
的图象的对称中心.已知函数
的图象的对称中心为
,讨论函数
的单调性并求极值.
(2)已知函数
,其中
.
(i)求
的拐点;
(ii)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408b5fe83aaebc38dad12ce4078e92e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)经研究发现所有的三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc8cd0533cd510418a9e367d2045ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da77290fb789fc7addf96dcc72a3f851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f18b54d3f22c0f4cf5d5ce0a968c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9ce9991b7db23119c4edac0dc42afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a8695cb53f51d16e2c0adbdfe029a2.png)
您最近一年使用:0次
2024-02-21更新
|
649次组卷
|
4卷引用:云南师范大学附属中学2023-2024学年高二下学期开学考试数学试卷