解题方法
1 . 设函数
,已知
是函数
的极值点.
(1)求
;
(2)设函数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594b7b3b82fd08473efd08cd4021c304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc027be769ea7e43c851e081fd8a0bf.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bbe149d1f40eefd9e8d98fa420f344.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd791cdf876b9a9e58f251f803aeb66.png)
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2 . 设函数
,
.
(1)当
时,求
的单调区间;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd8176f06a825620654b0c5a2fc9ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed85edaf5312e3482e661b1d20d80253.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)求
的极值点;
(2)设
,若对任意的
,都有
恒成立,求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b83f6440736816fbd005866d31b501d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eececc99fc28d96333f6c0f3e04ef742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6f04dea3fe074b903012e06b887e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 已知函数
,
(1)当
,求曲线
在
处的切线方程;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc41e4008ebf25d0b6ad99ba6e64b6a5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83de0f53d3366df7cfabbec91a934043.png)
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5 . 已知函数
,
.
(1)若
为
上的增函数,求
的取值范围;
(2)若
在
内恒成立,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed85e516715c0082cae32f1a09cc312e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ad04771eda0d7b0f4e14cf8d977c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
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2023-06-27更新
|
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6 . 已知函数
.
(1)若
,求
的单调区间;
(2)当
时,证明:
在
,
上各有一个零点,且这两个零点互为倒数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5172d0888b83e69fdec76676ac556f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85feaa0f6ce7f2926a66ebb864c57003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
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名校
解题方法
7 . 已知函数
.
(1)若
在
上单调递增,求实数a的取值范围;
(2)若
,使得
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9800c3c53c29e97ca1601e7f6395283e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f909328384f9c52134243753d9c954ef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae13fef7c52cac474116117af47d21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
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2023-06-14更新
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8 . 已知函数
.
(1)若
,求
的图象在
处的切线方程;
(2)若
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f137fe9ceb74c8aa2dbdd630c19cf645.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023·江苏南通·模拟预测
名校
解题方法
9 . 已知函数
,其中a为实数.
(1)若
,求函数
在区间
上的最小值;
(2)若函数
在
上存在两个极值点
,
,且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384295f05d99dedb5dcee82860226d63.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88080215d30285bf416853dd8f5b1365.png)
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10 . 已知函数
.
(1)设a=0.
①求曲线
在点
处的切线方程.
②试问
有极大值还是极小值?并说明理由.
(2)若
在
上恰有两个零点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f7ec07f4e97a53b23d98aa8fc6674d.png)
(1)设a=0.
①求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
②试问
![](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/49e1fcca51be2f5fea9bb06d0146fa50.png)
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