2021高三·全国·专题练习
1 . 设函数
,
.
(1)证明:当
时,
;
(2)判断函数
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab216f0238f359acaf0d3999ea6feb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5679281442e1788f4eb46c70ee5e347a.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f618d064463eb787ed097098cc860c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781a2a23602fcb21c897800e11bcdb4f.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57ddab9f0b4499413e0de4ee37bee34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4dbd480ab6b9de001b3e136b91c673.png)
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2021·全国·模拟预测
2 . 已知函数
,
.在下列三个条件中任选一个填在下面的横线上,解答下列问题.
①
,②
,③
.
(1)(ⅰ)______,曲线
在点
处的切线经过点
,求实数a的值;
(ⅱ)求证:
是曲线
的一条切线.
(2)
,当
,
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152903d460cecf097879a1807ddcfd44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d787b79077502bbb06424867bf58d47.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9cdea1e995c59e5d3225acad8b4d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9f817ad57fb668b829e18dfd21dc2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c69a18ac82d772e7c7707efe8f44eb6.png)
(1)(ⅰ)______,曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6715d5b63d9470c6e6980940141da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2ad636439e6572811bf1f98f853835.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae342dcb93e0e6f017093cacc5ac977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b66150793c738ead964a3ea4446a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011d5d2981f46dbe1769a6856d2560b4.png)
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2021-12-29更新
|
592次组卷
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3卷引用:江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷
江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷(已下线)2022届高三普通高等学校招生全国统一考试数学信息卷(二)四川省内江市第六中学2022届高三下学期考前第一次强化训练数学(理科)试卷
名校
解题方法
3 . 已知函数
.
(1)当
时,不等式
恒成立,求
的最小值;
(2)设数列
,其前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c126da234bfdf388845934f6a41416.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c31d9532638f0a36fb31f26c43884b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591a4b3ababc7b2025d0421530a7f53f.png)
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2020-09-05更新
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9卷引用:江苏省南通市如皋中学2020届高三创新班下学期高考冲刺模拟(二)数学试题
江苏省南通市如皋中学2020届高三创新班下学期高考冲刺模拟(二)数学试题2020届山东省淄博市高三一模数学试题甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题(已下线)专题八 函数与导数-2020山东模拟题分类汇编(已下线)强化卷01(4月)-冲刺2020高考数学之拿高分题目强化卷(山东专版)河北省衡水市衡水中学2022届高三上学期第二次调研数学试题河北省衡水中学2022届高三上学期二调数学试题(已下线)专题14 导数综合应用的解题模板-学会解题之高三数学万能解题模板【2022版】河北省沧州市沧州部分高中2024届高三上学期期中数学试题
4 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe71df7eac5e44cba50d2f2a8c26ee51.png)
.
(1)证明:
;
(2)若方程
有两个不等实根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ab948e5df77b57035f6b2717700858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe71df7eac5e44cba50d2f2a8c26ee51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3e3bcd67cf1a355986c6e3132470c7.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26449970128fa51a694ed908d84a994c.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1abf0cdd5f11934878e479ef1abfea64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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2卷引用:江苏省连云港市2021届高三下学期3.5模数学试题
5 . 已知函数
.
(1)若
是
的一个极值点,试讨论
在区间
上的单调性;
(2)设
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90db27e35b37e2d5dea8356e938e69da.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f56a20bc5fce6b02217627b42249854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c1fc90a6092b25ac0ee06fda1a7971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72d20f1bf6d42731872b4554cf81a03.png)
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2021-05-07更新
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607次组卷
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4卷引用:江苏省宿迁市2021届高三下学期第三次调研考试数学试题
名校
6 . 【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:江苏省南京师大附中2018届高三高考考前模拟考试数学试题
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(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)
7 . 已知函数
,且
在
上的最小值为0.
(1)求实数
的取值范围;
(2)设函数
在区间
上的导函数为
,若
对任意实数
恒成立,则称函数
在区间
上具有性质
.
(i)求证:函数
在
上具有性质
;
(ii)记
,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55386df48bce6389f5ea9dd827b2600d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a2bf55ddf8cf07f22b2128712e2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08653fc03ff2c4ccaf3ab8b18474ee17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9626dc41063c34f4243b5a637668b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88209b9c5c9503721afc5696b8943a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2f05512a14030b8a9cd9c118ed962f.png)
您最近一年使用:0次
8 . 若无穷数列
和无穷数列
满足:存在正常数A,使得对任意的
,均有
,则称数列
与
具有关系
.
(1)设无穷数列
和
均是等差数列,且
,
,问:数列
与
是否具有关系
?说明理由;
(2)设无穷数列
是首项为1,公比为
的等比数列,
,
,证明:数列
与
具有关系
,并求A的最小值;
(3)设无穷数列
是首项为1,公差为
的等差数列,无穷数列
是首项为2,公比为
的等比数列,试求数列
与
具有关系
的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd9630eef5312838c202cf054e9ee7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
(1)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e67d6abc5e1ab4c45046d1ee37e328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
(2)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2525f733e43b3a4558b83f10f20425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
(3)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d928d897331d22ce7a2d230ed7138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e116f14c30b56ba916164b2da784b4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
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2020-08-04更新
|
717次组卷
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4卷引用:江苏省南京师范大附中2020届高三下学期6月高考模拟(1)数学试题
江苏省南京师范大附中2020届高三下学期6月高考模拟(1)数学试题上海市青浦区2021届高三上学期一模(期终学业质量调研)数学试题上海市青浦区2021届高三上学期一模数学试题(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
名校
解题方法
9 . 设
是直线
与曲线
的两个交点的横坐标,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b8f1f4a005ada52c225801007495a9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7日内更新
|
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2卷引用:江苏省华罗庚中学2024届高三下学期5月适应性考试数学试卷
名校
解题方法
10 . 已知函数
,
.
(1)若
在
处取得极值,求
的值;
(2)设
,试讨论函数
的单调性;
(3)当
时,若存在正实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16382d2feded5c81e086989d46878ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980a8c4eb822aeb591ceacfe8a7aaa11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679353e656a54993c041ebd39ec7b31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924a99a014b343122d68282063aa0df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd330acca8e17f5ff9aca1f0f312df50.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36a91b78ea833d5b09c11366324a845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760effa3c34aefb5d6bbd0e7ca0d48fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4115c137af3720f88cba7557ce4e70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646abb51bfb8b5e30d0bb7cfe995a390.png)
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2018-11-18更新
|
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5卷引用:江苏省盐城市东台中学2018届高三学业质量监测数学试题
江苏省盐城市东台中学2018届高三学业质量监测数学试题山东省济南市历城第二中学2019届高三11月月考数学(文)试题(已下线)重难点突破05 极值点偏移问题与拐点偏移问题(七大题型)-2福建省“宁化、永安、尤溪、大田、沙县一中”五校协作2024届高三上学期11月联考数学试题新疆石河子市第一中学2024届高三上学期11月月考数学试题