名校
解题方法
1 . 已知函数
,若函数
有唯一极值点,则实数
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9525bdfdf009cebece1bd76a526c204e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-05-02更新
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303次组卷
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4卷引用:重庆市南坪中学2020-2021学年高二下学期期中数学试题
重庆市南坪中学2020-2021学年高二下学期期中数学试题黑龙江省哈尔滨市南岗区实验中学2021-2022学年高三上学期数学(理)第三次月考(开学考)试题四川省绵阳南山中学2023-2024学年高二下学期期中考试数学试题(已下线)专题6 指数、对数同构问题【讲】(高二期末压轴专项)
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2 . 已知函数
.
(1)当
时,讨论函数
的单调性;
(2)若不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aab6c3b4fed26aad712919ba41a808e.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157ea7510d828a967d304850126fd557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9da785604605f9af11b329328542aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-01-31更新
|
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5卷引用:湖南省株洲市第一中学2022届高三上学期期末数学测试卷
3 . 已知点S是圆
上任意一点,过S作x轴的垂线,垂足为H,点T满足
,记点T的轨迹为C.
(1)求轨迹C的方程;
(2)设轨迹C与x轴的交点分别为
,
,与y轴正半轴的交点为B,M是轨迹C上任意一点,且M不在坐标轴上.若直线
与直线
交于点P,直线
与直线
交于点Q.试判断
的形状,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13c02c5acb8df76da6356e504ded016.png)
(1)求轨迹C的方程;
(2)设轨迹C与x轴的交点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
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名校
解题方法
4 . 已知函数
,
,且曲线
和
在原点处有相同的切线.
(1)求实数a的值:
(2)证明:当
时,
;
(3)令
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82677d95bc109795e16401461dc6467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591d032abe536b6bfc4e04104dc921bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)求实数a的值:
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9e96e2ed7d9cd25c06f9a51a7210a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d3ac6f2ecceac9566cdc98752ba2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343143dd8a6ce47f1ea1a32478a8a49e.png)
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|
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2卷引用:黑龙江省大庆市大庆实验中学2021年高三上学期10月月考数学试题
名校
5 . 已知函数
,
(1)当
时,求函数
在
处的切线方程;
(2)讨论函数
的单调性;
(3)当函数
有两个极值点
且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5facb7583ea00e6d8db952d80557f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.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)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b314f6ccb0a3e4fc15685d85e55bf6.png)
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14卷引用:福建省宁化第一中学2022届高三9月第二次月考数学试题
福建省宁化第一中学2022届高三9月第二次月考数学试题广东省梅州市东山中学2022届高三上学期期中数学试题天津市第五十五中学2021-2022学年高三上学期10月学情调研数学试题云南衡水实验中学2022届高三上学期期中考试数学(理)试题黑龙江省哈尔滨工业大学附属中学校2021-2022学年高二上学期期末考试数学(理)试题(已下线)2020年高考天津数学高考真题变式题16-20题(已下线)第13讲 双变量问题-2022年新高考数学二轮专题突破精练河南省洛阳市洛宁县第一高级中学2022-2023学年高二下学期2月月考数学理科试题江苏省南京大学附属中学2022-2023学年高二下学期3月月考数学试题广西壮族自治区梧州市苍梧中学2022-2023学年高二下学期3月月考数学试题天津市五区县重点校2022-2023学年高二下学期期中联考数学试题(已下线)模块五 专题5 期中重组卷(广东)天津市滨海新区塘沽第一中学2024届高三上学期第一次月考数学复习卷2(已下线)导数专题:导数与不等式成立问题(6大题型)-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第二册)
名校
解题方法
6 . 已知在
中,
.证明:
(1)
;
(2)
在
上恒成立;
(3)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a98e220a9a1f2a1caa37e4cf4e213.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5e4691210486a560c59df09937d9f8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991a6e773c41687e5b13d36da7612e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb222ce13688da6fc57089ebf5812b0e.png)
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名校
解题方法
7 . 如图,已知抛物线
,
为其准线.
为
上一动点,过点
作
于
,直线
交抛物线于点
.若直线
过定点
.
(1)求
的值;
(2)过抛物线
上一动点
作抛物线
的两条切线,切点为
、
.记
的外心为
.证明:以
为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a9efe4c27ce894634c9e4c737b5fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb50782b4a4f59f8798a90086b0d5c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74973a2eb4281a6943a506b779740ca7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/2/c8b920e2-0711-4e77-866a-534d8d8da985.png?resizew=126)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b57041b43206fc0d477f8c769078f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d48de5a380ae57e1094720433ab1d54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303eb7923a91dcecc2d9bc1133d5c5d.png)
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8 . 已知
,则下列说法正确的有______ .
①若
有且仅有一个零点,则
;
②若
有且仅有一个零点,则
;
③若
有且仅有两个零点,则
;
④若
有且仅有一个极值点
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f33dfa2e69a4d9cf93797b1f95c0a8e.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db0eb7b60e88da1d807797cb17f85d0.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65f98fb31af1299a4d4b31d67a240b0.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe33a19334467abffbd1f79ab245ce4e.png)
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9 . 设函数
,记函数
有且仅有n个互不相同的零点(
),则当n取到最大值时,实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb47838693fde4afcc7627e6c74df02a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e0a9e336769fba32ab7b516f52d0a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
10 . 在直角坐标系xOy中,已知点
,直线AM,BM交于点M,且直线AM与直线BM的斜率满足:
.
(1)求点M的轨迹C的方程;
(2)设直线l交曲线C于P,Q两点,若直线AP与直线AQ的斜率之积等于-2,证明:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9e61a7c470be817b2de725460ddd66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298fa44e15f92fc6b5fc90eee2b019b2.png)
(1)求点M的轨迹C的方程;
(2)设直线l交曲线C于P,Q两点,若直线AP与直线AQ的斜率之积等于-2,证明:直线l过定点.
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2023-05-31更新
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2卷引用:2.4.2直线与圆锥曲线的综合问题 2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册