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1 . 已知函数
.
(1)讨论
的单调性;
(2)若方程
有两个不相等的根
,且
的导函数为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fc2a19b46639a8c5ed29281a867ba73.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e924f5b6b26534b7eea00660e9d0d9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133c30d6ca96a4d8de293da20fbe8f22.png)
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2 . 如图,一块边长为
正方形铁片上有四个以
为顶点的全等的等腰三角形(如图1),将这4个等腰三角形裁下来,然后用余下的四块阴影部分沿虚线折叠,使得
,
重合,
,
重合,
,
重合,
,
重合,
,
,
,
重合为点
,得到正四棱锥
(如图2).则在正四棱锥
中,以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb26c5cdef6f16f4b39cd091041b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a5faf3cbb633fc4294c8ce703c64c3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/12/cd2a3d46-4c9b-40be-bbdc-f857393ba3d8.png?resizew=150)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/12/832ab7b5-56a4-4f09-b565-e3bc9ee5d76d.png?resizew=187)
A.平面![]() ![]() |
B.![]() ![]() |
C.当![]() ![]() |
D.当正四棱锥的体积取到最大值时,![]() |
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名校
解题方法
3 . 已知,
,
,则( )
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
4 . 已知函数
,
.
(1)若函数
在
处的切线的斜率为
,求实数a的值(e是自然对数的底数);
(2)若函数
有且仅有两个零点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e2277b76a72fb7b96dbdd713a21198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c629b0c7a5005cd81845ad5c20bd0a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5 . 若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629a998d1e32d64daee9d2e9287eae10.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 定义函数
,其中
.
(1)当
时,求曲线
在点
处的切线方程;
(2)证明:在区间
上,
有且只有两个不同的极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26dfc40f7f470d3d7cff59fcdd7b5568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20611e8dc649c55a330103553a54f356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b212e0d4339cbd3d236a807547ebf6.png)
(2)证明:在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8c4008d33613ee4a86255f876722ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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7 . 已知定义在
上的函数
,若
的图象与
轴有3个不同的交点,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b531c04fedcd9539eef63e53c60cbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1c426f823fe5a9318807cb3e7d2df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cb12dd110ecdf90b3075ffd4209e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若
,设
是
的两个极值点,求证;
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2160f53364f0baced3778e340d39149.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/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81acc03f559e796903ca0c5ccb9b452.png)
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贵州省贵阳市2023届高三上学期8月摸底考试数学(理)试题贵州省黔南州2023届高三上学期摸底数学(理)试题河南省北大公学禹州国际学校2022-2023学年高三上学期第一次月考理科数学试题(已下线)专题08 导数及其应用(讲义)-2江苏省盐城市亭湖高级中学2022-2023学年高三上学期第一次摸底考试数学试题(已下线)河南省济源市、平顶山市、许昌市2022届高三文科数学试题变式题21-23
名校
9 . 已知
.
(1)求函数
的单调区间;
(2)若函数
有两个零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786999ff39b91fac93044fb70679be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8112293429caa01e7670ebcaf5bf95de.png)
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10 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)若
,
,
,请比较a,b,c的大小;
(2)若函数
有两个零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233aa8bb190d5535f84eade0cfbc6b95.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ccdf28e62c595d1f0337b18d70266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba48368ed6dd4b0f6d49b30113de0f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a90f10037c5230d4281abb93c9179e4.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786999ff39b91fac93044fb70679be5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b67a008cbc20e42a317acfd632a8052.png)
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