名校
解题方法
1 . 定义在
上的函数
满足
,
(若
,则
,c为常数),则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0a028f1d7bffc087f345909ddbb498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4915a7b17389ab1238077f4c4ee8f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11fa3246d1f5f3859c61f03f3387cd0a.png)
A.![]() |
B.![]() ![]() ![]() |
C.![]() |
D.若![]() ![]() ![]() |
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解题方法
2 . 已知函数
.
(1)当
时,请判断
的极值点的个数并说明理由;
(2)若
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ec761e879aa6a6a25ee87106270529.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79863748bbb4f280cdbfd58bb94b84dd.png)
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名校
解题方法
3 . 已知
为实数集
的非空子集,若存在函数
且满足如下条件:①
定义域为
时,值域为
;②对任意
,
,均有
. 则称
是集合
到集合
的一个“完美对应”.
(1)用初等函数构造区间
到区间
的一个完美对应
;
(2)求证:整数集
到有理数集
之间不存在完美对应;
(3)若
,
,且
是某区间
到区间
的一个完美对应,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c42648f413abc4ec6b042f0924e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7ee80da08376cb9a6f0ac641b2d1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)用初等函数构造区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f14df2d8d1fea71da4197e81b6ee3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求证:整数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067802ecb7978511f798ef27d02e890b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ecb1589c3cc179e2f62507020771e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8835e96965b13d49dd1481403eb997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e2bb6cfd4b2fa49622dc9b7c39b62b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
4 . 已知函数
.
(1)当
时,求
的极值;
(2)若
恒成立,求实数
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d0dffe17c575a4feb86c28d97182a7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b245ba1efcc5776b03e8669fa30da8aa.png)
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名校
解题方法
5 . 已知函数
.
(1)当
时,求函数
的极值;
(2)求函数
的单调区间;
(3)当
时,若
在
时恒成立,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a884c696e802c2962004fdf519482b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1749eb0942146be0ef6c0b39a33d8b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/6463b3ff9900061f267f612d3d2b7633.png)
A.函数![]() |
B.若方程![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
解题方法
7 . 已知函数
.
(1)若
,求
的极值;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6249f1f1e3736630f08af86c0301a40.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f113db8bfea6f3a482c168738a43437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
8 . 已知函数
.
(1)
在定义域内单调递减,求
的范围;
(2)讨论函数
在定义域内的极值点的个数;
(3)若函数
在
处取得极值,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7c6dbd23c3a97ca565293fa527a43c.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)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/c8c2d34cb1ea0cf34812cd7bf01a37b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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名校
9 . 已知
(其中
为自然对数的底数).
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,判断
是否存在极值,并说明理由;
(3)若对任意实数
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04d21bd20b782e1b1a030b04d8394fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66367f83e841caba04d29fceaa5cf4f7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9baa33e282d8b0b45c68b268ac610044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
10 . 已知定义在
上的函数
,其导函数为
,且
若关于
的不等式
仅有
个整数解,则实数
的取值范围是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed80d5c7d9b1ad4cb887a4e1be345f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1710aefca8c70a3098ddddb35a8775f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4695e7ce5d4fbedb2ba790f70af0224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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