名校
解题方法
1 . 已知函数
的图象在点
处的切线方程为
.
(1)求
在
内的单调区间.
(2)设函数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e662da6fc6c0e0e910df301b8b061a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea05a2396e436b4df62d6328dbeaddc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0461093ce098b7a99076bbd4f04512.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df5334ec4482e12a0ba4d7773ed9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d465075757811c815c9d637a3e119a8.png)
您最近一年使用:0次
2021-11-26更新
|
688次组卷
|
11卷引用:江苏省扬州市江都区邵伯高级中学2021-2022学年高三上学期期末热身测试一数学试题
江苏省扬州市江都区邵伯高级中学2021-2022学年高三上学期期末热身测试一数学试题广东省部分学校2022届高三上学期11月大联考数学试题河北省保定市部分学校2022届高三上学期期中数学试题湖南省百校大联考2021-2022学年高三上学期11月联考数学试题陕西省西安交大附中2021-2022学年高三上学期12月月考理科数学试题内蒙古霍林郭勒市第一中学2021-2022学年高二下学期期中考试数学试题广西2023届高三上学期开学摸底考试数学(文)试题广西柳州市鹿寨县鹿寨中学2023届高三上学期开学摸底考试数学(文)试题(已下线)专题2-4 导数证明不等式归类(讲+练)-1福建省泉州科技中学2023届高三上学期期中考试数学试题【押题金卷】2022年普通高等学校招生全国统一考试理科数学试卷(A卷)
2 . 已知函数
.(
是自然对数的底数)
(1)若
,
,求不等式
的解集;
(2)若
,证明:对任意
,
成立;
(3)若
,试讨论函数
的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d974067fc61270a83b1320af368ba53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec7d442dcd50c38bb6966d3822738f8.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
3 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedd7be672b179eaf072f53635fe130b.png)
_____ ;若直线
(
)与函数
的图象有交点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd0690b529099376398a467c9c0612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedd7be672b179eaf072f53635fe130b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd0690b529099376398a467c9c0612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
4 . 已知函数
,
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
在区间
上有唯一的零点
.
(ⅰ)求
的取值范围;
(ⅱ)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e13a7b4412b076ce06d657bad7cc174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14e4bcfe3a9c89a8d19a73e259e2b42.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15bccf9756ec716bd5c04e2641b6441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f99bddac58806e0024a1268378fe53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86324ac8bce57770ee879111ee71f2b.png)
您最近一年使用:0次
20-21高三上·江苏南通·期末
解题方法
5 . 已知函数
,
.
(1)若关于.
的不等式
对任意的
恒成立,求实数
的取值范围;
(2)设
,
.
①求证:
;
②若数列
满足
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc142c4a9f9c8505e7824361a9003099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(1)若关于.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2475f4a516b408e9c1a1f81bc013b71f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7780ab2eba3eaa3d391a8d5ee712485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2788f2efd111b65f7458002508765c56.png)
②若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4b41419ce9ed61c73bfe422e738c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2c8eb8fd8d5ad456dcf7c3e3279da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d77a6078beed1d99f07c5cbb5ff4484.png)
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2021·全国·模拟预测
名校
6 . 已知函数
.
(1)讨论
的零点个数;
(2)当
时,设
的极值点为
,一个零点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997f6bb9588f4781d77ab7de62de8385.png)
(1)讨论
![](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/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0ae0f481c131cdb0422a0a87872d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599b3c1da7979306b834d55f967e431b.png)
您最近一年使用:0次
名校
7 . 【江苏省南京师大附中2018届高三高考考前模拟考试数学试题】已知函数f(x)=lnx-ax+a,a∈R.
(1)若a=1,求函数f(x)的极值;
(2)若函数f(x)有两个零点,求a的范围;
(3)对于曲线y=f(x)上的两个不同的点P(x1,f(x1)),Q(x2,f(x2)),记直线PQ的斜率为k,若y=f(x)的导函数为f ′(x),证明:f ′(
)<k.
(1)若a=1,求函数f(x)的极值;
(2)若函数f(x)有两个零点,求a的范围;
(3)对于曲线y=f(x)上的两个不同的点P(x1,f(x1)),Q(x2,f(x2)),记直线PQ的斜率为k,若y=f(x)的导函数为f ′(x),证明:f ′(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d12e47079a6f07bb6eff6c9e14401da.png)
您最近一年使用:0次
2018-05-30更新
|
1530次组卷
|
3卷引用:江苏省南京外国语学校仙林分校中学部2017—2018学年度高二下学期期末测试(理科)数学试题
江苏省南京外国语学校仙林分校中学部2017—2018学年度高二下学期期末测试(理科)数学试题江苏省南京师大附中2018届高三高考考前模拟考试数学试题(已下线)专题19 导数的应用-2018年高考数学(理)母题题源系列(江苏专版)
名校
解题方法
8 . 已知函数
,
.
(1)若
在
上单调递减,求实数
的取值范围;
(2)当
时,求证
在
上恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafe4e0c76faa18fc4b8d2acc786fd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b61adc4745f283e4072ddd762f92ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665e92c365730c03e3bc94aed79a1058.png)
您最近一年使用:0次
2021-08-08更新
|
524次组卷
|
3卷引用:江苏省无锡市2020-2021学年高二下学期期末数学试题
名校
解题方法
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8ca8ea93e01e9e0f0c3e4aa5425448.png)
(1)当
时,求函数
在
处的切线方程;
(2)设
,若
在
上单调递增,求实数
的取值范围;
(3)设
,若存在不相等的实数
,
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8ca8ea93e01e9e0f0c3e4aa5425448.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/a9c81965854dbe52a513241f196edf2c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14423a12f7f8d3125da44cd9be25036b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04f5684d862b1be1f8883838fa93b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1dcdfce4e67213937b00a44b0c8412.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/2492d486aef92677bc4d9c88c28b6845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38b06319904c858b4e36f4731cfee6d.png)
您最近一年使用:0次
2020-08-10更新
|
710次组卷
|
2卷引用:江苏省泰州市2019-2020学年高二下学期期末数学试题
10 . 已知函数
,其中,
是自然对数的底数,
.
(1)当
,
时,求证:
;
(2)若函数
有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e07cb92d1939cb10ba83d9f00590651.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/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee18d7a40f7a7e0dc85b1bd75bf750c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6000b174147cec2de26041837aec1b3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次