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1 . 下列不等式中正确的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:河南省濮阳市2024届高三第三次模拟考试数学试题
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2 . 已知
,函数
.
(1)当
时,求
的单调区间;
(2)当
时,设
的导函数为
,若
恒成立,求证:存在
,使得
;
(3)设
,若存在
,使得
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fef330410912ad36677dbf8549b7f7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0953444691256f713639f4ded91ff306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990ea00761500cbd2a51283a2f443421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c72d250a079379c5175693c165248c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f8f8ab529ff605ee0c00e551a01622.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ae80746de8e491dcb8df4b1c42dbea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478052f005a72e660f55b439e77955dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c247baa451cd7868d97daa7103085ae.png)
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5卷引用:天津市部分区2023届高三二模数学试题
天津市部分区2023届高三二模数学试题(已下线)第九章 导数与三角函数的联袂 专题三 含三角函数的恒成立问题 微点3 三角函数的恒成立问题(三)新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题(已下线)专题6 导数与零点偏移【练】(已下线)2024年天津高考数学真题平行卷(提升)
3 . 若函数
的图象上的若干个不同点处的切线互相重合,则称该切线为函数
的图象的“自公切线”,称这若干个点为函数
的图象的一组“同切点”例如,如图,直线
为函数
的图象的“自公切线”,
,
为函数
的图象的一组“同切点”.
在
处的切线为它的一条“自公切线”,求该自公切线方程;
(2)若
,求证:函数
,
有唯一零点,且该函数的图象不存在“自公切线”;
(3)设
,函数
,
的零点为
,求证:
为函数
的一组同切点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.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/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556995a9d28d7755aa28d18fcdf82386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2d0b8cd2c080211babbefe92a8969b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4ee7e0a6461d1d6636e376bfa9b275.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe02c554d7141801d82ae5b12a8ad8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4757efc8199c12b32f07b11d4ddb9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce603aa3abcb61750d2191aaa13dddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309b41172ad8049ec30a81c6fdc1e502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556995a9d28d7755aa28d18fcdf82386.png)
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4 . 已知椭圆
的长轴为4,直线
与圆
相切于点
,与
相交于
,
两点,且
,
,
.
(1)记
的离心率为
,证明:
;
(2)若
轴右侧的点
在
上,且
轴,
,
是圆
的两条切线,切点分别为
,
(
在
上方),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4966973694e3fdf6b63434b7bee5911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd6303756adb878c1e028f511e51f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32a5bdae1e1c0082553d71b80dbcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a16563ac359fda8ac16989aa704b23.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af72fe2d8fdcd6793597db51d070290e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b79e16fb149b3ea933cd087f0cc740.png)
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名校
5 . 已知函数
.
(1)若
,讨论
的零点个数;
(2)若
是函数
(
为
的导函数)的两个不同的零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a441ed40dca1a0f8c5ed0253d1ca300.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab42358409a44ea7a55fe532fe66ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550cb121a3346f8d46b7f7ee2117d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380beb181ed0a48cc486131bba4a4c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d106beb9c7a567f35e7f3407f41c963c.png)
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3卷引用:河南省焦作市2024届高三第二次模拟考试数学试题
6 . 已知抛物线
的焦点为
,在
轴上的截距为正数的直线
与
交于
两点,直线
与
的另一个交点为
.
(1)若
,求
;
(2)过点
作
的切线
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,则当
的面积取得最小值时,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a68ce9569af419362238f6f24f5a5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc094d6bccc3b13a496b9c3a423f737.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:河南省焦作市2024届高三第二次模拟考试数学试题
7 . 已知函数
,点
为平面内一点,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cbc38dede229ac885633f63550e685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493f7a6fe5c1e676672547297082e64d.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.若过点![]() ![]() ![]() ![]() |
D.若过点![]() ![]() ![]() ![]() |
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8 . 已知函数
的图象与直线
有三个交点,记三个交点的横坐标分别为
,且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ed60f0cb88418ef55dbaca23275611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64deec46e463ce6c2ee4d3f24b96e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
A.存在实数![]() ![]() |
B.![]() |
C.![]() |
D.![]() |
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10卷引用:广东省华南师范大学附属中学2023届高三三模数学试题
广东省华南师范大学附属中学2023届高三三模数学试题河南省南阳市第一中学校2024届高三上学期期末模拟数学试题贵州省贵阳市第一中学2024届高三上学期高考适应性月考卷(五)数学试题江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(三)(已下线)专题23 导数及其应用小题(已下线)思想02 运用数形结合的思想方法解题(4大核心考点)(讲义)广东省2024届高三数学新改革适应性训练五(九省联考题型)重庆市部分学校2023-2024学年高二下学期4月阶段检测数学试题(已下线)专题5 指数对数同构问题(过关集训)(压轴题大全)河南省信阳市新县高级中学2024届高三考前第五次适应性考试数学试题
名校
解题方法
9 . 设函数
,
.若
在
恒成立,则实数
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d3b7babdd3c6e84fb9d5025d825b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d64ccef2aba16e16307139224b55a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fce924911d5ed93147dfce9e41c2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5卷引用:广东省中山市中山纪念中学2024届高三上学期第三次模拟测试数学试题
广东省中山市中山纪念中学2024届高三上学期第三次模拟测试数学试题云南省德宏傣族景颇族自治州2024届高三上学期期末教学质量监测数学试题广东省广州市广东实验中学2024届高三上学期第三次调研数学试题(已下线)5.3.2课时2函数的最大(小)值 第三练 能力提升拔高(已下线)专题5 指数对数同构问题(过关集训)(压轴题大全)
10 . 若函数
在
上单调递增,则a和b的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7a98b117e51c5fa3028888e37fd515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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5卷引用:湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题