真题
解题方法
1 . 已知
,
是函数
的图象上两个不同的点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a05181414c221b7c7ce0d72fa3c7125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8fd6e8a27cf393cb3894aba173dc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90881c8738b1298210fa761f789a55db.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7卷引用:专题02函数
专题02函数(已下线)2024年北京高考数学真题变式题6-10专题03函数概念与基本初等函数(已下线)五年北京专题02函数概念与基本初等函数(已下线)三年北京专题02函数概念与基本初等函数(已下线)五年北京专题01集合、常用逻辑与不等式2024年北京高考数学真题
真题
2 . 对于一个函数
和一个点
,令
,若
是
取到最小值的点,则称
是
在
的“最近点”.
(1)对于
,求证:对于点
,存在点
,使得点
是
在
的“最近点”;
(2)对于
,请判断是否存在一个点
,它是
在
的“最近点”,且直线
与
在点
处的切线垂直;
(3)已知
在定义域R上存在导函数
,且函数
在定义域R上恒正,设点
,
.若对任意的
,存在点
同时是
在
的“最近点”,试判断
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e75192ed6ee73f295754edfbbb4a4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25be20e3724274132cb83b16deaeecfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6085b118b86f7f4dd54864e113cd595c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7bce420cf236e5f429afee284239010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3641338ac7fd85ef574690ba1f988d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6be4ab05ff885a4a6a043eaebe7a91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf6463a6ee745687de1ee10f4d40253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90183525765a8279328417af4bf6179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237c115d5b39d761e1cbcae031070b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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3 . 已知函数
,若
,则当
取得最小值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1817297374e431a1d9087dcc2991d3a9.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e863ea4f1e8af63d06ad88a235a48f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9f81c0a84cd2c60891b1d71de2dbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45437e5332f864582b88474569adf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1817297374e431a1d9087dcc2991d3a9.png)
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名校
解题方法
4 . 在
中,角A,B,C所对的边分别为a,b,c.若
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e8370a3c1802256270059fd6f4b207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23511ccf4ac3f865d3f3a830dc55a5da.png)
A.![]() | B.![]() | C.![]() | D.4 |
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昨日更新
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535次组卷
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5卷引用:核心考点3 解三角形与实际应用 A基础卷 (高一期末考试必考的10大核心考点)
(已下线)核心考点3 解三角形与实际应用 A基础卷 (高一期末考试必考的10大核心考点) (已下线)【高一模块一】难度7 小题强化限时晋级练 (较难1)(已下线)解三角形-综合测试卷B卷河南师范大学附属中学2024届高三下学期最后一卷数学试题江苏省泰州市2024届高三下学期四模数学试题
2024高三·全国·专题练习
5 . 已知锐角
中,内角
所对的边分别为
,
,
,点D在边AC上,且
,过点D分别作边AB,BC的垂线,垂足分别为M,N,设
,
,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e29b822cda1ba926e96368094fa1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb0e2b72fd7c6e8c2cc491478904497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa42e19b955697300513537121bad1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d895f5ad97c70ee49712f63804c4ecf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717a38d02651c3a40f41ed3f56a1da1e.png)
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6 . 已知
分别为
的边
上的点,线段
和
相交于点
,若
,
,
,其中
.则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be878f5bdce9a3e9939a4ae743c803b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1174877b02d3c54c58314fa7cd1218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83463cbe4e6b434ce448c053cae70ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761e8ff96c96ac26682b521288a01bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c227da7ad9d24ae3e3740febf9f293.png)
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2024高三·全国·专题练习
解题方法
7 . 已知
,若
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ec4a082d54487fb3b8dc3547d21d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a17022d499b5b7626683891e338dc9d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 如图,在
中,点
为边
上靠近
点的三等分点,
,
.
,求三角形
的面积;
(2)当
最小时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bdcd23d2c26d9df0b4756d8a715673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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9 . 已知样本数据为1,a,b,7,9,该样本数据的平均数为5,则这组样本数据的方差的最小值为______ .
您最近一年使用:0次
名校
10 . 设
是
内一点,且
,定义
,其中
分别是
的面积,若
,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f58ff77bc49f127a27e0af56573944c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801d50da9a58b1b1d48141e6ad01c1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b511bcbe94aa484c0a067891fbf7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d201ead127c65cc0bc153fdb445e420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4d96a8d81b2cd450bd92e7a9ec791f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f257b71e2b7886aadf7f1ebc809c10b1.png)
A.![]() | B.18 | C.16 | D.9 |
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507次组卷
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5卷引用:核心考点2 平面向量的数量积 B提升卷 (高一期末考试必考的10大核心考点)
(已下线)核心考点2 平面向量的数量积 B提升卷 (高一期末考试必考的10大核心考点)(已下线)核心考点3 解三角形与实际应用 A基础卷 (高一期末考试必考的10大核心考点) (已下线)【高一模块一】难度7 小题强化限时晋级练 (较难1)福建省三明市六校2023-2024学年高一下学期期中联考数学试卷四川省南充市南部中学2023-2024学年高一下学期第二次月考数学试题