9-10高三·湖南湘潭·阶段练习
名校
解题方法
1 . 已知二次函数
对
都满足
且
,设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079f277788b447aabb0b527020dc20a4.png)
(
,
).
(1)求
的表达式;
(2)若
,使
成立,求实数
的取值范围;
(3)设
,
,求证:对于
,恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad5fe274cfc8da2dacfb65801f344ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb38ca84b4eadbe4eaa09bb5c778d912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1feffb0bb2658090edd0b2f9f2721fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079f277788b447aabb0b527020dc20a4.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bf7d03f075e1c0a67d02a56ddd6611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86aada6c0797463dd75408a0ad45c43e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e07a024c9ae1e811ea066430c02fd62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd1b5a2a71ae12061e768a1814f536a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e0e6b300b63f5424deaa89734811f.png)
您最近一年使用:0次
2 .
为自然对数的底数.
(Ⅰ)求函数
在区间
上的最值;
(Ⅱ)当
时,设函数
(其中
为常数)的3个极值点为
,且
,将
这5个数按照从小到大的顺序排列,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632e88f116c6097af475a688705cfd14.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fc7213b26c42d036c1badbd1670e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dd6536acc4fc34c218ff759e3a0ee7.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6b6aa80882b83ad1965f69f5d448d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d976762e69c7e36275880e0be76442c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3079295dfca242a49094c64b0dc8b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e3f13980284fcf2e7615fad83211cd.png)
您最近一年使用:0次
名校
解题方法
3 . 设函数
.
(1)若函数
在
上单调递增,求
的取值范围;
(2)当
时,设函数
的最小值为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf316d7b9027a4b6827dd92615db727f.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a7b7c834d06f3e28a339db94690172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0523c2e025e1b9060fd8eb09ac07a9.png)
您最近一年使用:0次
2016-12-04更新
|
311次组卷
|
4卷引用:2015-2016学年辽宁省鞍山一中高二下期中理科数学试卷
4 . 已知函数
.
(Ⅰ)求函数
的单调区间;
(Ⅱ)当
时,已知
,且
,求证:
.
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182572466176/1572182578208768/STEM/03ac175ae9564008820e81fda9ca70dc.png)
(Ⅰ)求函数
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182572466176/1572182578208768/STEM/105524b4a2594a339d0700958e8b215e.png)
(Ⅱ)当
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182572466176/1572182578208768/STEM/b1622ca3589b4285ad021f2806901706.png)
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182572466176/1572182578208768/STEM/a42c5b4376ea46088575bd6a982634e7.png)
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182572466176/1572182578208768/STEM/1857da3e3c7e4dc58dad348376719f36.png)
![](https://img.xkw.com/dksih/QBM/2015/7/15/1572182572466176/1572182578208768/STEM/f3b68344b5ba4d4fb7e57738453be7d5.png)
您最近一年使用:0次
名校
5 . 已知函数
.
(1)求函数
的单调区间;
(2)已知
,
,(其中
是自然对数的底数),求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b26f55c7c29644dfe0277d3e2adf10.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18478e45096362e297359fe9345b073a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fd5a05aae4f1a7d8a8e32e80ca7263.png)
您最近一年使用:0次
2016-12-03更新
|
562次组卷
|
6卷引用:辽宁省沈阳市东北育才学校2018-2019学年高二下学期期中考试数学(理)试题
真题
名校
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a8517145a2c2a2c20ce70d39e0155.png)
(I)求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e01806dfeedf652a5c8c43901c5812.png)
(II)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00526521c2ac6ac9ba4a775740bd0d6e.png)
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a8517145a2c2a2c20ce70d39e0155.png)
(I)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e01806dfeedf652a5c8c43901c5812.png)
(II)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00526521c2ac6ac9ba4a775740bd0d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef37bad50fd1567f50541827fae1d812.png)
您最近一年使用:0次
2016-12-02更新
|
4206次组卷
|
9卷引用:2013年全国普通高等学校招生统一考试理科数学(辽宁卷)
2013年全国普通高等学校招生统一考试理科数学(辽宁卷)2016届湖南省长沙市长郡中学高考模拟一理科数学试卷【校级联考】广东省六校2019届高三第三次联考理科数学试题江苏省扬州市新华中学2020-2021学年高三上学期第一次月考数学试题(已下线)第二篇 函数与导数专题3 洛必达法则 微点1 洛必达法则吉林省长春吉大附中实验学校2023-2024学年高三上学期第一次摸底考试数学试题(已下线)第六章 导数与不等式恒成立问题 专题十一 利用洛必达法则解决不等式恒成立问题 微点1 利用洛必达法则解决不等式恒成立问题(1)(已下线)题型07 3类导数综合问题解题技巧(已下线)专题14 洛必达法则的应用【练】
2011·山东济南·高考模拟
7 . 已知函数
.
(1)讨论函数
的单调性;
(2)当
时,
恒成立,求实数
的取值范围;
(3)证明:![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/5c11ffcdb3b243e49c38f954da781766.png)
.
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/6dfb89e2ec6140f399b74eb615d7c0b6.png)
(1)讨论函数
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/499e6f85a3bd4ea7b0bf7112369c3d81.png)
(2)当
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/901504716ac244d5a0a29830644e25c7.png)
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/afae38b617694a07b79d608d446aa606.png)
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/7ed7735d6810419ab2ac64fed31dde89.png)
(3)证明:
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/5c11ffcdb3b243e49c38f954da781766.png)
![](https://img.xkw.com/dksih/QBM/2011/7/27/1570276313448448/1570276319182848/STEM/4d7a60c2d5dd48f193d4048b8b286638.png)
您最近一年使用:0次
10-11高二下·辽宁·期中
8 . 已知函数
.
(1)若
,求证:函数
有且仅有
零点;
(2)若关于
的不等式
在
上恒成立,其中
是自然对数的底数,求实数
的取值范围.
参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f43a1fcaeb4a25ac37f7751427744c6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1392fd6b0ee7cc4a48fdab46fb51a619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd27b57c7dd68b9efc05e3d807015ea9.png)
您最近一年使用:0次
9-10高三·山东·阶段练习
名校
9 . 已知函数
在
处取得极值.
(Ⅰ)求函数
的解析式;
(Ⅱ)求证:对于区间
上任意两个自变量的值
,都有
;
(Ⅲ)若过点
可作曲线
的三条切线,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fccec26803c270b8e22f77099bb12a9d.png)
![](https://img.xkw.com/dksih/QBM/2010/9/30/1569846864535552/1569846869401600/STEM/a4cd0e5fc1754b7aa9daeee366a3ee39.png)
(Ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)求证:对于区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291d664e9ea8088c35bb6b0550f18675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://img.xkw.com/dksih/QBM/2010/9/30/1569846864535552/1569846869401600/STEM/597336be786d4ca6af652f84ec52a9e0.png)
(Ⅲ)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26820332294b112e27b8d7ffa4ae8631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-11-30更新
|
1366次组卷
|
7卷引用:2015届辽宁省大连市第二十高级中学高三上学期期中考试文科数学试卷
(已下线)2015届辽宁省大连市第二十高级中学高三上学期期中考试文科数学试卷辽宁省实验中学营口分校2019-2020学年下学期期中考试高二数学试题(已下线)2010-2011学年永春一中、培元中学、季延中学和石光华侨联中高三第一次统考数(已下线)2011届广东省深圳高级中学高三上学期期中考试数学理卷(已下线)2011—2012学年度黑龙江大庆实验中学高二上学期期末考试文科数学试卷河南省林州市第一中学2019-2020学年高二(实验班)4月月考数学试题(已下线)专题04 三次函数的图象和性质-1
名校
解题方法
10 . 已知函数
.
(1)若
在
处取得极小值,求
的值;
(2)若
在
上恒成立,求
的取值范围;
(3)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6391131de160fd6a96724d70c43a36.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cd36edcc1439abfb8daa649ee3512e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130ab7a635323d182a0da76e9fe25aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece1cabeedc0da3de06bd8b7753cdf52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd18e15beae3d49de756f416bc89d885.png)
您最近一年使用:0次
2016-12-05更新
|
991次组卷
|
3卷引用:2017届辽宁鞍山一中高三上一模考试数学(理)试卷