名校
解题方法
1 . 已知函数
.
(1)求函数
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ce04a52818f54d0bf8d63c822dcf.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6790f1010defae05e26f1ab6ce62f1e1.png)
您最近一年使用:0次
2022-06-06更新
|
699次组卷
|
3卷引用:辽宁省沈阳市东北育才学校2021-2022学年高二下学期6月月考数学试卷
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f851ef31c02e0c4f056383b2a5c96026.png)
(1)讨论
的单调性;
(2)证明: ①当
时,函数
有两个零点;
②当
时,函数
一个零点;请从①②中选择其一作答.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f851ef31c02e0c4f056383b2a5c96026.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明: ①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0b5b6968f2ea9b927e5c39182fa508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70899d59387c6bce1a5db07597597eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
3 . 已知函数
.
(1)若
,求a的值;
(2)当
时,从下面①和②两个结论中任选其一进行证明.
①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701f9c6fe4a64a8a55a5c0b97cac85e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e71bfb38628fc8a11ac5f22a0c4eb5f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c625e2b0b47d94730d5319a40348a68d.png)
您最近一年使用:0次
2022-04-27更新
|
1449次组卷
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5卷引用:辽宁省沈阳市2022届高三下学期二模数学试题
辽宁省沈阳市2022届高三下学期二模数学试题湖南省岳阳市2022届高三下学期教学质量监测(三)数学试题(已下线)2022年高考考前最后一课-数学(正式版)-2022年新高考数学终极押题卷辽宁省大连市2022届高三第一次模拟考试数学试题(已下线)技巧04 结构不良问题解题策略(5大题型)(练习)
名校
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
(1)判断函数
的单调性,并比较
与
;
(2)设方程
的两个根为
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b842c8f63970a0cd302017ae1eef5720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2748b5620b52169c5cf05c8df92f7340.png)
(2)设方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/341058ba41688b6c7253c4ca2cad0cd1.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/d39a533560863efecd642f0476fe8a38.png)
您最近一年使用:0次
解题方法
5 . 已知函数
和
.
(1)当
时,求方程
的实根;
(2)若对任意的
,函数
的图象总在函数
的图象的上方,求实数
的取值范围;
(3)求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc3ee9845a1a0329311d0c56f326704a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/659dd220350b3f94539c7914709516aa.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6330540758a21f46fc7a6d1e6328d8.png)
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a412fdc7d0161ec1f6f70da328c2e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
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2021-09-23更新
|
626次组卷
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7卷引用:辽宁省沈阳市郊联体2021-2022学年高三上学期期中考试数学试题
辽宁省沈阳市郊联体2021-2022学年高三上学期期中考试数学试题2018届高三数学训练题(25 ):导数 苏教版(2019) 选修第一册 突围者 第5章 全章综合检测人教B版(2019) 选修第三册 突围者 第六章 素养拓展北师大版(2019) 选修第二册 突围者 第二章 全章综合检测(已下线)5.3 导数在研究函数中的应用(重点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)2023版 苏教版(2019) 选修第一册 突围者 第5章 全章综合检测
6 . 已知函数
有两个零点
,
,且
.
(1)求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c207efd83d75c1f69237d97616c726.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)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8f867196410e2828e2bbd3183b02d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次
名校
7 . 已知函数
,其中
.
(1)讨论函数
在
上的单调性;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9c3403d1565f1e1ea345ab5ad003c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b01772d8f82f005d37da05c0ad5355.png)
您最近一年使用:0次
2022-02-27更新
|
851次组卷
|
4卷引用:辽宁省沈阳市东北育才学校2021-2022学年高二下学期期中考试数学试题
名校
8 . 已知函数
,
.
(1)讨论
的单调区间;
(2)当
时,令
.
①证明:当
时,
;
②若数列
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeea9bb195a844feb2f1806db8259604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ee7c7dd3a775fa701366908859c614.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd791cdf876b9a9e58f251f803aeb66.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6f4a302d3a9023c0a82b889f4ba918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92903b4ad4fc018c9f7d0309ed20403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63554d67f64c68adbd28bce22fb79b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7378e6e95cfe560f97ec0e7951e15a.png)
您最近一年使用:0次
2022-03-04更新
|
3799次组卷
|
9卷引用:辽宁省沈阳市第一二O中学2022-2023学年高三上学期期末数学试题
21-22高三上·北京·期中
名校
9 . 设函数
,其中
.
(1)若
是函数
的极值点,求a的值;
(2)当
时,求函数
的单调区间;
(3)当
时,设函数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a2789aa3ed49a69c3c68e590ee9950a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](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/9b3cdc842b6aad995999de2712688c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a06acf17d7c28fa264c03224226951b.png)
您最近一年使用:0次
名校
10 . 设函数
,
.
(1)求函数
的单调区间;
(2)若方程
有两个不相等的实数根
、
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd468a555d0651540a1328047325d4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0104b0f55b45d14cf478c11589eb39.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/1f13e5c66b641e6f5bfddff5d1997a34.png)
您最近一年使用:0次
2021-08-22更新
|
1709次组卷
|
6卷引用:辽宁省沈阳市东北育才学校 2021-2022学年高三上学期第一次模拟考试数学试题