1 . 设函数
,其中
R.
(1)若a=0,求过点(0,﹣1)且与曲线
相切的直线方程;
(2)若函数
有两个零点
,
.①求a的取值范围;②求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1524cc6426cd0fad327fb5fd4ce1e5c.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45638ae62892b6fdec7b1048097805a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb71310ec267ea2c2fc0ccaeb2343d0.png)
(1)若a=0,求过点(0,﹣1)且与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/d1524cc6426cd0fad327fb5fd4ce1e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37708a68d0ca72413ada85d01d2ed19.png)
您最近一年使用:0次
2018-02-01更新
|
630次组卷
|
5卷引用:江苏省南京市2017-2018学年高二上学期期末考试数学理试题
江苏省南京市2017-2018学年高二上学期期末考试数学理试题【全国校级联考】江苏省姜堰、溧阳、前黄中学2018届高三4月联考数学试题【市级联考】江苏省无锡市2019届高三第一学期期末复习数学试题(已下线)2017-2018学年度下学期高二数学期末备考总动员C卷理科01(已下线)2017-2018学年度下学期高二数学期末备考总动员C卷文科01
20-21高三上·江苏南通·阶段练习
名校
解题方法
2 . 已知函数
,
,若
在
处取得极小值.
(1)求实数
的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d511ddc6f723be68c45d0cde2290bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2367b48e8f6dbbfe3dd14f6eab8238a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7971bee02d30d2de09df26a61222f198.png)
您最近一年使用:0次
2020-10-21更新
|
260次组卷
|
5卷引用:江苏省南通市如皋市2020-2021学年高三上学期10月第一次教学质量调研数学试题
(已下线)江苏省南通市如皋市2020-2021学年高三上学期10月第一次教学质量调研数学试题江苏省南通市海门市包场高级中学2020-2021学年高三上学期10月第二次阶段检测数学试题(已下线)2021届高三高考数学适应性测试八省联考考后仿真系列卷一广西壮族自治区防城港市2023届高三下学期4月月考数学(理)试题四川省绵阳市绵阳南山中学实验学校2022-2023学年高三下学期4月月考数学理科试题
11-12高三下·江苏淮安·开学考试
名校
3 . 已知
.
(1)若函数
在区间
上有极值,求实数
的取值范围;
(2)若关于
的方程
有实数解,求实数
的取值范围;
(3)当
,
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5220c1d29955df47343122a463c46a92.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b6bec0e5c57dc0c97d2581012d2c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cf6b77ccc80b271e6b41231c740da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e6a4a1d228a9eec9db8080bef34231.png)
您最近一年使用:0次
2016-12-01更新
|
1340次组卷
|
3卷引用:2012届江苏省淮阴中学高三下学期数学综合练习(1)
(已下线)2012届江苏省淮阴中学高三下学期数学综合练习(1)江苏省淮安市淮阴中学2019-2020学年高三下学期4月综合测试数学试题江苏省盐城市滨海中学2019-2020学年高二下学期期末模拟数学试题
名校
4 . 已知函数
,
.
(1)求
的单调区间;
(2)证明:
;
(3)若关于x的方程
有唯一解,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66571e342cc898db23de0e0b9d4df7cc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17e6d6609ca6f99872ace43a64b38f40.png)
(3)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
您最近一年使用:0次
2020-08-10更新
|
281次组卷
|
2卷引用:江苏省南通市名师2020届高三下学期最后一卷数学试题
名校
解题方法
5 . 已知函数
(
)的图象上的动点
到原点
的距离的平方的最小值为
.
(1)求
的值;
(2)设
,若函数
有两个极值点
、
,且
,证明:
.(参考公式:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85dec0e14a423774ee0c60c09482544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe977fffd09723b3d649a201bcd91f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdc63f1ba98019281322bf82eee6b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b20d307c8466cccab12fd7adfe6506.png)
您最近一年使用:0次
2020-04-11更新
|
281次组卷
|
3卷引用:江苏省苏州市昆山震川高级中学2020届高三下学期三模数学试题
江苏省苏州市昆山震川高级中学2020届高三下学期三模数学试题2020届河北省保定市高三第一次模拟数学(文)试题(已下线)调研测试五(A卷 基础过关检测)-2021年高考数学(文)一轮复习单元滚动双测卷
6 . 设函数
(
为自然对数的底数,
).
(1)当
时,求函数
的图象在
处的切线方程;
(2)若函数
在区间
上具有单调性,求
的取值范围;
(3)若函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d327f3c96cc14952bb3b5aa8354965ac.png)
有且仅有
个不同的零点
,且
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2307a0b4a1258a4e62a31ed86f4db3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d327f3c96cc14952bb3b5aa8354965ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc69e53616dbd12a8d5d780ed3d84a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fcdccdff3319c45eee064c89c18810.png)
您最近一年使用:0次
11-12高二·湖南湘西·阶段练习
名校
解题方法
7 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3b6c56aee4bb8a8131fd960415c745.png)
.
(1)求函数
的最小值;
(2)设
,讨论函数
的单调性;
(3)斜率为
的直线与曲线
交于
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
两点,
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3b6c56aee4bb8a8131fd960415c745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03556c333ab0b55fe86c937b2a5763.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffb1a5cc934731fa849d2af47d805c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
(3)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d3c0e7508ff7fd36faba07a0aa41ff.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70898d64ac02d8800d02d8aab7653ff.png)
您最近一年使用:0次
2016-12-01更新
|
1509次组卷
|
7卷引用:江苏省苏州新草桥中学2019-2020学年高二下学期期中数学试题
8 . 已知函数
,
.
(1)若
,求函数
的单调区间;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e74da4b06c434c46d5a8958ad77f2592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c6398b022655e7ae74515ef717178.png)
您最近一年使用:0次
2020-04-08更新
|
287次组卷
|
4卷引用:第三章 导数及其应用(能力提升)-2020-2021学年高二数学单元测试定心卷(苏教版选修1-1)
(已下线)第三章 导数及其应用(能力提升)-2020-2021学年高二数学单元测试定心卷(苏教版选修1-1)2020届辽宁省丹东市高三3月线上教学质量监测数学(文)试题(已下线)第五章++一元函数的导数及其应用1(能力提升)-2020-2021学年高二数学单元测试定心卷(人教A版2019选择性必修第二册)(已下线)第三章+导数及其应用(能力提升)-2020-2021学年高二数学单元测试定心卷(人教版选修1-1)
解题方法
9 . 已知
.
(1)若
,求函数
的单调区间和最小值.
(2)若
有两个极值求实数
的取值范围.
(3)若
,且
,比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a8c377f111a3e504bceb29effc1037.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/2018/7/1/1979222041640960/1981094176833536/STEM/c32de3da465a4a20b9b42c08d05369cb.png?resizew=10)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fba7172c836e73177e47d7daecc28bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895a921249ca11c61d751228920ea2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e9458b51c4c643607b45a249fa99ac.png)
您最近一年使用:0次
2018-07-04更新
|
482次组卷
|
2卷引用:江苏省扬州市2017~2018学年高二第二学期期末试卷(文科 )
名校
解题方法
10 . 已知函数
,
(
为常数).
(1)若函数
与函数
在
处有相同的切线,求实数
的值;
(2)若
,且
,求证:
;
(3)若对任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3b6c56aee4bb8a8131fd960415c745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0088f91cbfd9e441e586d6805f0a3828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(1)若函数
![](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/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce2594833690eedb3328fe747feb3a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2017-04-08更新
|
1004次组卷
|
4卷引用:【全国百强校】江苏省启东中学2018-2019学年高二下学期期中考试数学试题