名校
解题方法
1 . 已知函数
.
(1)若
的极小值为-4,求
的值;
(2)若
有两个不同的极值点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec485b17e78ee033856963013d5dec5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20a11121e7ccc795552da69bb921071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06e1fc0c843262c1463d9cf04bb835.png)
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名校
解题方法
2 . 曲线
在点
处的切线的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3540cc9b8c18d270ea9b016ae0926f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6a8fe1c12aacc7396a4b9526671c80.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
3 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)讨论函数
的单调性;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba17f18c17d3d9f4145022baeb5c72bb.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
4 . 已知函数
.
(1)当
时,求
的图象在
处的切线方程;
(2)若函数
存在单调递减区间,求实数a的取值范围;
(3)设
是函数
的两个极值点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ce03991003cf95131016408f2d4ce1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d06e33d079ac1649ee5eea8f61de7cf.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcad362a59670d52247deb8af650927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648d45539fbee959eabbf7a6c01f6982.png)
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5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
时,求
的零点;
(2)若
恰有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7日内更新
|
473次组卷
|
5卷引用:吉林省吉林市第一中学等校2023-2024学年高二下学期5月期中联考数学试题
名校
解题方法
6 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beff0aabd2bb1fe031b658c55258ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db30ad779d5ff572a140cd6e3b0d3c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d75280bf1f91ea4d4d806d604d36977.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-14更新
|
640次组卷
|
4卷引用:吉林省吉林市第一中学等校2023-2024学年高二下学期5月期中联考数学试题
名校
解题方法
7 . 已知
为方程
的根,
为方程
的根,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb0bd07a0eec6d37efe8f2e310b5420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06143cdf12d19aa34f0a1e60feeb787.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-06-13更新
|
292次组卷
|
3卷引用:吉林省吉林市第一中学等校2023-2024学年高二下学期5月期中联考数学试题
名校
解题方法
8 . 已知函数
,且满足
,则实数
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d54554cce9ab9d1ae528d4ae30dbb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9192e24be965dccb0ecf7f945c9bae81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 已知函数
(其中
),
.
(1)当
时,求函数
的图象在点
处的切线方程;
(2)当
时,若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce470994a9e4e013d895240a8923bdda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdad8acb5f4d31bfee990bf844b1a37.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-06-08更新
|
1290次组卷
|
2卷引用:吉林省长春市第二中学2023-2024学年高二下学期5月期中考试数学试题
名校
10 . 已知函数
,则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4668987b91f6aad9312c2ccebb33ac.png)
A.![]() |
B.![]() |
C.若方程![]() ![]() |
D.若![]() ![]() |
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