名校
1 . 已知
.
(1)若
在
处取到极值,求
的值;
(2)直接写出
零点的个数,结论不要求证明;
(3)当
时,设函数
,证明:函数
存在唯一的极小值点且极小值大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f77abf65029bf4014dfea70aded594.png)
(1)若
![](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/0a6936d370d6a238a608ca56f87198de.png)
(2)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5be3af0c67a20bee47063487d305f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
您最近一年使用:0次
名校
解题方法
2 . 设函数
,
.
(1)求
在
上的最值;
(2)若函数
图象恰与函数
图象相切,求实数
的值;
(3)若函数
有两个极值点
,
,设点
,
,证明:
、
两点连线的斜率
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603589540f7897790f99a8d75fd725f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5602d1637fb9dab9ef09ae6030b4ed7d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10bb9a8107bd9c4f083578f473b9a99.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/67a3f0d7706dd7b38b770656f6937776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210304b08abfee9be4e4d3b01e323a66.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/b387bb66f74a73d9f08c79e77a4df771.png)
您最近一年使用:0次
2024-06-04更新
|
235次组卷
|
2卷引用:海南省文昌中学2023-2024学年高二下学期期中段考数学试题
3 . 已知函数
,且
的图象在
处的切线斜率为2.
(1)求m;
(2)求
的单调区间;
(3)若
有两个不等的实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f02ec33f2caccc63110feeef0ab275e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec25b105130d71d3d529524671b6218.png)
(1)求m;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70f5b3ed05b816949d8811d5956ae0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4f5a04663e6ea4d0f183d27a6ba59.png)
您最近一年使用:0次
4 . (1)证明:当
时,
;
(2)若过点
且斜率为
的直线
与曲线
交于
两点,
为坐标原点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468ddff079eafd5b6062e230f8ed42a.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0482468ee9123843cc9310b1fd7a27b4.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)当
时,求
的单调区间与极值;
(2)若
,证明:当
,且
时,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5594f2712521f9910abf07039850b5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec5792dbdc5ee1677ecd53435552272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e32125207addc3fdb92ceb0ec80ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a620b284ae80049376c7a7c9afab1f62.png)
您最近一年使用:0次
2023-12-22更新
|
748次组卷
|
3卷引用:海南省2024届高三上学期一轮复习调研考试(12月联考)数学试题
解题方法
6 . 已知函数
,
的导函数为
.
(1)若
在
上单调递减,求实数
的取值范围;
(2)当
时,记函数
的极大值和极小值分别为
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f249e584f96d9445d5f198df66317956.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afbf5885d0a84f158684ac3dbd517fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5cdde751120c6deab563a6f7f8cf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7dd0dee94372d2c25fd92ee22dc577.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,
.
(1)证明:对于
,
,都有
.
(2)当
时,直线
:
与曲线
和
均相切,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3199e7b4e66aba9f167701839e94e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfe02fb63c8d651466881d4b85a45b9.png)
(1)证明:对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129450a089ab2e252cd3e229b22df4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-09-19更新
|
632次组卷
|
5卷引用:海南省琼海市嘉积中学2023届高三三模数学试题
8 . 已知函数
的导函数为
.
(1)若
,求曲线
在点
处的切线方程.
(2)若
存在两个不同的零点
,
(ⅰ)求实数
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e15ecb3e777a4767f56bb7ceb105d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.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/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c701c5c07f7c584aadd218d9e341d3ac.png)
您最近一年使用:0次
名校
解题方法
9 . 英国数学家泰勒发现了如下公式:
其中
为自然对数的底数,
.以上公式称为泰勒公式.设
,根据以上信息,并结合高中所学的数学知识,解决如下问题.
(1)证明:
;
(2)设
,证明:
;
(3)设
,若
是
的极小值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6696028290bbaddf628d64bad0ed95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2976d45a26ec77149a05553e8eb13efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78478b44ff22e088fd8e6522c5d78a2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d84ae7f43ef85da907d2917ff5f2a80.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8586154d8c4fb5fef893d39a7701f921.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde823e2e88ecb6045d66d61962259b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-03更新
|
2338次组卷
|
19卷引用:海南省海南华侨中学2023-2024学年高三下学期第二次模拟考试数学试题
海南省海南华侨中学2023-2024学年高三下学期第二次模拟考试数学试题贵州省贵阳市2024届高三下学期适应性考试数学试卷(一)贵州省安顺市2024届高三下学期模拟考试(一)数学试卷云南省玉溪市第一中学2023-2024学年高二下学期3月月考数学试题重庆市礼嘉中学2023-2024学年高二下学期第一次月考数学试题吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题重庆第十一中学校2023-2024学年高二下学期3月月考数学试题重庆市璧山中学校2023-2024学年高二下学期第一次月考数学试题广东省东莞市光明中学2023-2024学年高二下学期第一次月考数学试题四川省达州外国语学校2023-2024学年高二下学期3月月考数学试题黑龙江省哈尔滨市双城区兆麟中学2023-2024学年高二下学期第一次月考(4月)数学试题重庆市荣昌中学校2023-2024学年高二下学期4月期中考试数学试题广东省广州市广州中学2023-2024学年高二下学期期中考试数学试题江西省宜春市上高二中2024届高三下学期5月月考数学试卷(已下线)专题11 利用泰勒展开式证明不等式【练】河北省石家庄四十一中2023-2024学年高二下学期第一次月考数学试题河北省石家庄二中润德中学2023-2024学年高二下学期第一次月考数学试题福建省宁德市古田县第一中学2024届高中毕业班高考前适应性测试数学试题四川省南充市白塔中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
10 . 已知函数
,且
在
处取得极值.
(1)求a;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ce6bdb1a8271f7f1a640f91a32a4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(1)求a;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ac88fba12e6a16206a3e9edf6b7abe.png)
您最近一年使用:0次
2023-09-21更新
|
277次组卷
|
2卷引用:海南省琼中黎族苗族自治县琼中中学2024届高三上学期9月高考全真模拟卷(一)数学试题