1 . 已知函数
和
.
(1)若函数
在点
处的切线与直线
垂直,求
的单调区间和极值;
(2)当
时,证明:
的图象恒在
的图象的下方.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf88f7ec79fc9e89f1806e1d027d69a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1610bcd07b02c4ed7184ad586b88f373.png)
(1)若函数
![](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/a9e493a2a0d0c1c4cd3c334454419d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561800aa679a45da4dbe0e323de1fd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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2 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)当
时,求
的极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3d31b1ff6b85a44ff9525706423bf3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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名校
解题方法
3 . 已知函数
.
(1)当
时,证明:
.
(2)试问
是否为
的极值点?说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3eb38deba5a3008e2ee5026b7d2865.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99923994f2c1721fc07450b4b9656980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c5fdeae3d9934cbc3f916bd7fbf496.png)
(2)试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2024-01-09更新
|
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4卷引用:贵州省黔东南苗族侗族自治州2024届高三12月统测(一模)数学试题
名校
4 . 已知函数
的定义域为
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d655d4e9f91965bd0d1dfb142e27824.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5卷引用:贵州省六盘水市2023-2024学年高三上学期第二次联考数学试题
5 . 已知函数
.
(1)求
的极值;
(2)已知
,且
,用函数
性质证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafb94c1205634b96a4042a7cb7facc5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84624ddb3f05c1d41e6fc24db2a4ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895a921249ca11c61d751228920ea2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6bf3b4facf23aa0582a20822a4fbafd.png)
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6 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2292c63db8e6aacd0bb3050e3075e482.png)
A.![]() ![]() ![]() |
B.![]() |
C.当![]() ![]() |
D.若函数![]() ![]() ![]() |
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4卷引用:贵州省黔东南州从江县2024届高三上学期11月检测数学试题
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解题方法
7 . 已知函数
,
.
(1)求函数
的极小值;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331c29cbc908d8aa91d85809437d9f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9489607c09fa9b0e8ea1a00beb9bf3d4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92acace17d43431c5d414cdc3b624fe2.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
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2卷引用:贵州省2024届高三适应性联考(一)数学试题
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8 . 已知函数
.
(1)求函数
在
处的切线方程;
(2)若过点
存在3条直线与曲线
相切,求
的取值范围;
(3)请问过点
,
,
,
,
分别存在几条直线与曲线
相切?(请直接写出结论,不需要证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553e916cbe7f202d8c400aef83b99391.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aefcf9299f5c114ef8a072d3279d625.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)请问过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb9e88d3e58141dba299dcd8edc4e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb6fd712d967a36c027693a54f91470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f12f12b6e78f741846da2d56089631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947bca78fd2d7a7436dd9dedbba3baa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b08c0db034208fc9cdc0e7e7817f321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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3卷引用:贵州省黔西南州部分学校2024届高三上学期9月高考适应性月考(一)数学试题
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c45d730f7de4d2534217e165831454.png)
(1)求
的极值;
(2)当
,
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c45d730f7de4d2534217e165831454.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef6a9bc8be0f6d89596d91f8c2b3dd8.png)
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名校
10 . 已知函
(
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a551216f6cb0b0157d140720d42473aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若函数![]() ![]() |
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2023-09-03更新
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