1 . 已知函数
.
(1)若
,证明:曲线
在
处的切线与直线
垂直;
(2)若
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6845a29100f7ffb8c3ad1d820592031a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d494dd08ea05abf7e99261b6f05efc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6d40b58666f8c945938aa0d1e8f6b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad71d89cb1213d8796e1ee84fd171e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08de6d63f3dc41dea59ac1cbd16e8d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1db0ce92b8b408198b4ac4d1ad2ee2e.png)
您最近一年使用:0次
2 . 已知函数
,
.
(1)若函数
在区间
上单调递减,试探究函数
在区间
上的单调性;
(2)证明:方程
在
上有且仅有两解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558f93b58a11ac52301f4d64e14f501f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d502d9d892310a0d19dd1dd1675991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)证明:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acd884552ee3aaecf68b8dca5a41e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
您最近一年使用:0次
解题方法
3 . 已知函数
.
(1)若
在
处的切线与直线
垂直,求
的极值;
(2)设
与直线
交于点
,抛物线
与直线
交于点
,若对任意
,恒有
,试分析
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e6adf3a3caed3ddd73b23416ba5755.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/8095fdb64e12a270cb61135e29507f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8f7fd7368e184037e99934ee9171be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e452b96dc36b30641488388e77851e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac67e9a909472ab852d38d2ec66a1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)若
在
处的切线与直线
垂直,求
的极值;
(2)若函数
的图象恒在直线
的下方.
①求实数
的取值范围;
②求证:对任意正整数
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5d7bf46fe9b64f762ebcd347d155fb.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/957446b2f02eeaf2a1e29794036f1131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②求证:对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ba7d30c23e7ff46853402a9a8a0334.png)
您最近一年使用:0次
2020-03-18更新
|
345次组卷
|
2卷引用:山西省临汾市2020届高三下学期模拟考试(2)数学(理)试题
10-11高三上·四川成都·阶段练习
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddf6074f37be64268c8d65363ec0654.png)
(1)求
的单调区间和值域;
(2) 设
,函数
,
,若对于任意
,总存在
,使得
成立,求
的取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddf6074f37be64268c8d65363ec0654.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2) 设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70d86bd0030efbfde863536640fb0045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5d499666f20047af33ad30482efd37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc0414f6c290d1dc3678ba41b4620f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982f44059061490f50329f7e71aa0dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-01-30更新
|
866次组卷
|
5卷引用:山西省临汾市洪洞县第一中学2020届高三上学期期中数学(理)试题
名校
6 . 设函数
.
(1)当
时,求
的单调区间;
(2)若当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0775c7f80ffd673e261b450e46f9007e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f498b6874410fb46e9807e04371e6e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2018-07-25更新
|
453次组卷
|
4卷引用:【全国百强校】山西省临汾第一中学校2017-2018学年高二下学期期末考试数学(文)试题
名校
7 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed3b6866d53432ea1cc4b29ea9b0188.png)
(1)讨论
的单调性;
(2)设
是
的两个零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed3b6866d53432ea1cc4b29ea9b0188.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574824d85f44d42246529ac135c0391c.png)
您最近一年使用:0次
2018-05-25更新
|
7807次组卷
|
13卷引用:【全国百强校】山西省临汾第一中学2017-2018学年高二下学期期末考试数学(理)试题
【全国百强校】山西省临汾第一中学2017-2018学年高二下学期期末考试数学(理)试题【全国市级联考】湖南省益阳市高三理数5月18日统考试卷【全国校级联考】福建省百校2018届下学期临考冲刺高三数学考试卷数学理科(已下线)2018年高考题及模拟题汇编 【理科】2.函数与导数【全国百强校】黑龙江省鹤岗市第一中学2018-2019学年高二下学期期中考试数学(理)试题湖南省怀化市2018-2019学年高三下学期期末博览联考数学(理)试题山西省太原市2019-2020学年高三上学期期末数学(理)试题山西省朔州市怀仁县怀仁一中云东校区2019-2020学年高二下学期期末数学(理)试题(已下线)极值点偏移专题02 极值点偏移问题判定定理(已下线)极值点偏移专题04含参数的极值点偏移问题河南省三门峡市外国语高级中学2020-2021学年第一学期高二期中考试数学试题(已下线)专题16 导数妙解极值点偏移、双变量问题-备战2022年高考数学一轮复习一网打尽之重点难点突破山东省济南市天桥区黄河双语实验学校2022-2023学年高三上学期9月月考数学试题
名校
8 . 已知函数
,
(1)讨论函数
的单调区间;
(2)求证:
;
(3)求证:当
时,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcda8385f9ceac2bc360320d3e2f0891.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743f43accc9e4c271896b3411e0df10a.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006dd721f6e19ee105cf6e3a10b69c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a8de478b4c7988d7edd88a3320866a.png)
您最近一年使用:0次
2018-03-15更新
|
712次组卷
|
6卷引用:山西省临汾一中、忻州一中、长治二中、康杰中学2016-2017学校高二4月联考数学(文)试题
9 . 设函数
,
.
(1)若函数
在
上单调递增,求
的取值范围;
(2)设
,点
是曲线
与
的一个交点,且这两曲线在点
处的切线互相垂直,证明:存在唯一的实数
满足题意,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226c6f419ddc9d4e0f4b103cdc5fe661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e663a09cdcde628b5633a6ab07dd55b.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4bac43b27bfcdc3e3e26ee812eae83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93627eb4bfb9bea2a87ce92a237d9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbcc0dfa8adbb4e9952f72c4b26cc441.png)
您最近一年使用:0次
2018-02-22更新
|
336次组卷
|
2卷引用:山西省临汾第一中学等五校2017-2018学年高二上学期期末联考数学(理)试题
2011·山东青岛·一模
10 . 已知函数
.
(Ⅰ)若
,令函数
,求函数
在
上的极大值、极小值;
(Ⅱ)若函数
在
上恒为单调递增函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f123437102a4c01d8aec6a15d09b8c.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be7892193e97bf330eec0782dfb18fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/795ee91678ad50ac0bf3ae6dea537d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0052c5c876a5351b1fb3a69dba1e6cf.png)
(Ⅱ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/346f4e371a0268d852f4a770aab6eb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次