解题方法
1 . 已知定义在
上的两个函数
,
.
(1)若
,求
的最小值;
(2)设直线
与曲线
,
分别交于
,
两点,当
取最小值时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734c7b2eb046e56290605d91a8062f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914a49b0d7aedc593a3e87fbab7c31ca.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7b188eb70e0796813bb29b47d534fd.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2 . 已知函数
在
上可导且
,其导函数
满足:
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33875cdd9542d54912febef6b02d014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281bb4da5c83fd6c6f95bd1d30524600.png)
A.函数![]() |
B.函数![]() |
C.当![]() ![]() |
D.![]() ![]() ![]() |
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2024-02-08更新
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1369次组卷
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5卷引用:山西省临汾市2024届高考考前适应性训练考试(一)数学试题
山西省临汾市2024届高考考前适应性训练考试(一)数学试题(已下线)信息必刷卷01(已下线)模块2 专题3 构造函数 解不等式练(高考真题素材库之典型好题母题)(已下线)信息必刷卷04(江苏专用,2024新题型)辽宁省大连育明高级中学2023-2024学年高二下学期期中考试数学试卷
解题方法
3 . 在
中,点D在
上,
,
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c700a22bbc79eb6d1c1f3a2e89825a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7f89fd7ddc3277cf27230a12d60f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a41d6b52d491ce10ded1278947112927.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知关于
的方程
有且仅有两解
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac48a54e9ab010ee13a07eec6950e757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
A.函数![]() ![]() |
B.![]() |
C.![]() ![]() |
D.存在唯一![]() ![]() |
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2022-11-01更新
|
662次组卷
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4卷引用:山西省临汾市等联考2023届高三上学期期中数学试题
山西省临汾市等联考2023届高三上学期期中数学试题湖南省长沙市第一中学2022-2023学年高三上学期月考(五)数学试题(已下线)江苏省七市2022届高三下学期第二次调研考试数学试题变式题11-16江西省上饶市六校2022-2023学年高二下学期5月联考数学试题
12-13高三下·北京海淀·期末
名校
解题方法
5 . 已知函数
,点
为一定点,直线
分别与函数
的图象和
轴交于点
,
,记
的面积为
.
(Ⅰ)当
时,求函数
的单调区间;
(Ⅱ)当
时,若
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a903745cd2cb536443d07579b606ece5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12994e38fd2490f572790ca8a44bb1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a9fc2dda89829fa2c610a8fce86d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf37898700f118daeac10fe61b10c43.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf37898700f118daeac10fe61b10c43.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8989d48a405c4de0f83595085be32d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a64a0ac20caed06af9bb7dcaad2515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-05-09更新
|
636次组卷
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5卷引用:2014届山西省曲沃中学高三上学期期中考试理科数学试卷
(已下线)2014届山西省曲沃中学高三上学期期中考试理科数学试卷(已下线)2013届北京市海淀区高三5月期末练习(二模)理科数学试卷北京市陈经纶中学 2019-2020学年第二学期高二期中自主检测数学试题北京一零一中学2022届高三上学期统考(二)数学试题(已下线)北京市第四中学2023届高三上学期开学测试数学试题
名校
6 . 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)
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2018-05-25更新
|
7806次组卷
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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
7 . 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)
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2018-02-22更新
|
336次组卷
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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
10-11高三上·四川成都·阶段练习
名校
8 . 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)
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2019-01-30更新
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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
9 . 已知函数
.
(1)若曲线
在点
处的切线与曲线
的公共点的横坐标之和为3,求
的值;
(2)当
时,对任意
,使
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2dcee7e3151f3e58d0509c04fec4e8.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d983f1213ce474227e80c41d7fba6374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f88a76f947e7022ef0c5efd6db060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8311315b1ed5535f374125fe4a4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6038f1b0f1860b56cd62f397ad77a770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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