1 . 已知函数f(x)=lnx+a(x2+x),g(x)=x3+5x.
(1)讨论函数f(x)的单调性;
(2)当a=2时,证明:f(x)<g(x)﹣
.
(1)讨论函数f(x)的单调性;
(2)当a=2时,证明:f(x)<g(x)﹣
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
您最近一年使用:0次
2021高三·广东·专题练习
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d50055c5be921702b5f468d95ca6067.png)
(1)若
在区间
上存在极值,求实数
的范围;
(2)若
在区间
上的极小值等于0,求实数
的值;
(3)令
,
.曲线
与直线
交于
,
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d50055c5be921702b5f468d95ca6067.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9242dd26ba42e906d512542f02807779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9242dd26ba42e906d512542f02807779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173989eb4c71ba9a2c37740216473227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ed9bbf022719b29ae0b2ca587ab0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36312981a939667948c38c03fcca24ff.png)
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3 . 设函数
.
(1)当
时,讨论
在
内的单调性;
(2)当
时,证明:
有且仅有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2381e1f3b24b910359e96458710316d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1798ba947bed1f794c123106b8d5519.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442958bd5b5f8ac690b33ea0bccdd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
解题方法
4 . 已知
.
(1)设
是
的极值点,求实数
的值,并求
的单调区间;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3f353034d77c4117da65a096e88b75.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e07d5d11e230bf6e22a0317abbca335.png)
您最近一年使用:0次
2020-08-07更新
|
2046次组卷
|
17卷引用:【市级联考】辽宁省沈阳市2019届高三教学质量监测(三)数学(理)试题
【市级联考】辽宁省沈阳市2019届高三教学质量监测(三)数学(理)试题【市级联考】广东省汕头市2019届高三第一次模拟考试文科数学试题(已下线)2019年4月6日 《每日一题》理数选修2-2(期中复习)-周末培优【市级联考】江西省宜春市 2019 届高三4月模拟考试数学(文科)试题福建省莆田第一中学2018-2019学年高二下学期期中考试数学(文)试题2019届重庆市南开中学高考模拟(7)理科数学试题四川省仁寿第一中学校南校区2018-2019学年高二下学期期中数学(理)试题四川省仁寿第一中学校南校区2018-2019学年高二下学期期中数学(文)试题2020届宁夏石嘴山市高三4月二模数学(理)试题(已下线)专题03 利用导数求函数的极值、最值(第六篇)-备战2020年高考数学大题精做之解答题题型全覆盖(已下线)专题05 函数与不等式相结合(第六篇)-备战2020年高考数学大题精做之解答题题型全覆盖2020年普通高等学校招生全国统一考试 文科数学样卷(六)(已下线)易错点12 模拟卷(一)-备战2021年新高考数学一轮复习易错题宁夏石嘴山市2020届高三适应性测试数学(理)试题(已下线)【南昌新东方】江西省南昌市南昌县莲塘一中2019-2020学年高二下学期4月网络考试文科数学试题河北省唐山市第一中学2020-2021学年高二下学期期中数学试题四川省成都市简阳市阳安中学2022-2023学年高二下学期5月月考数学(理)试题
5 . 已知函数
.
(1)讨论
的单调性;
(2)求证:当
时,
;
(3)设
是整数,对于任意的正整数
,有
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553d72d688e34a65beb6939061721c3f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0d2761b7298a62a7f56caef88ee3db.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952cdff30a13c7e9eeee8fdca17e5bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-07-26更新
|
420次组卷
|
2卷引用:辽宁省大连市2019-2020学年高二(下)期末数学试题
6 . 已知函数
,曲线
在点
,
(1)
处的切线方程为
.
(1)求函数
的解析式,并证明:
.
(2)已知
,且函数
与函数
的图象交于
,
,
,
两点,且线段
的中点为
,
,证明:
(1)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7471c6cd8a297e0a5005331037e24c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75a5a4a9a9572b06af878043c02e8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a63c52ed4d74feca1248b68657cdb4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28c0c0b1d8a4aba3693a95caf42d41b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec1718debe1c497bd0223cd6d5e668e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a54e0b4872cabdc0b07ea9380e4de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a350eb41c3b7e4face9c3299eff9d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8e72f73db207c3040f143d837d5995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24529eadaef974ec0625f8ca40682e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a2c44bd75911eb48101f4d63fa2ca5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb554264d6838229cf2920a9bd99cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b0352e8a9e8d9b8c547c7a11cddf6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71351fd32b9c3832ea85a05000cd0319.png)
您最近一年使用:0次
2020-06-23更新
|
3198次组卷
|
9卷引用:辽宁省抚顺市第一中学2020届高三第二次模拟考试数学(理科)试题
辽宁省抚顺市第一中学2020届高三第二次模拟考试数学(理科)试题湖南省益阳市桃江县第一中学2019届高三5月模拟考试理科数学试题2020届山东省临沂市临沭县高三上学期期末数学试题湖北省金字三角2019-2020学年高三下学期3月线上联考理科数学试题(已下线)专题05 函数与不等式相结合(第六篇)-备战2020年高考数学大题精做之解答题题型全覆盖湖北省金字三角2020届高三下学期高考模拟理科数学试题(已下线)第10讲 双变量不等式:中点型-突破2022年新高考数学导数压轴解答题精选精练(已下线)2022年高考考前20天终极冲刺攻略(一)【理科数学】(5月20日)(已下线)专题9:双变量问题
解题方法
7 . 已知函数
,
,
.
(1)当
时,若对任意
均有
成立,求实数k的取值范围;
(2)设直线
与曲线
和曲线
均相切,切点分别为
,
,其中
.
①求证:
;
②当
时,关于x的不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7c4adef3485e8ac6e50d1926365327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c41009905994507dae7224c1c7f870b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212983432fdb9bb12719fc9be4b410d1.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16552a1b3198b61e02f62592431cb583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d01c545537e6330e36a618706d7b92.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6073fc52cd10164c1313dd96069b8d00.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6637636cfad409d24add56c4ce53c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68bb186b90ea5f2ae009d4aa98083393.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)当
时,求曲线
与曲线
的公切线的方程;
(2)设函数
的两个极值点为
,求证:关于
的方程
有唯一解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9344d31cd373c0431c280462027e20bd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d486982dcad14c4a07c60a18580c47f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad139ab3bc571e4b71af43afc96a9cf4.png)
您最近一年使用:0次
2020-05-28更新
|
1091次组卷
|
5卷引用:辽宁省沈阳市东北育才学校科学高中部2021-2022学年高三上学期第三次模拟考试数学试题
辽宁省沈阳市东北育才学校科学高中部2021-2022学年高三上学期第三次模拟考试数学试题2019届浙江省温州市普通高中高三上学期8月高考适应性测试数学试题甘肃省白银市第一中学2020届高三5月模拟考试数学(文科)试题(已下线)2022年高考浙江数学高考真题变式题13-15题(已下线)2022年高考浙江数学高考真题变式题19-22题
解题方法
9 . 已知椭圆
的左、右焦点分别为
、
,直线
与椭圆
交于
、
两点,
,
为椭圆
上任意一点,且
的最大值为
.
(1)求椭圆
的方程;
(2)过椭圆
的上顶点
作两条不同的直线,分别交椭圆
于另一点
和
(异于
),若直线
、
的斜率之和为
,证明直线
恒过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c16eafcd77c758af3534886b1c8e365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/81ea0e7989a2709fdd0e9f89f9946d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3df14e8b1b02dbda69bfbb06269cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
名校
10 . 已知函数
.
(Ⅰ)当
时,求
零点处的切线方程;
(Ⅱ)若
有两个零点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9f97f7a85bf705634839ec09963826.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fd45000fe915a242d0e78a420068e3.png)
您最近一年使用:0次
2020-05-13更新
|
1589次组卷
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5卷引用:2020届辽宁省大连市高三下学期第一次模拟考试数学(理)试题
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