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1 . 对于函数
和
,给出下列四个结论:
①设
的定义域为
,
的定义域为
,则
是
的真子集.
②函数
的图像在
处的切线斜率为0.
③函数
的单调减区间是
,
.
④函数
的图像关于点
对称.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0876376d0abc78d4ad8c5bbc597bde35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5c5c59bc2375e93325755a09e40d77.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfdd3d02b54e997cbec983d80f6bafd.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b6da436d60628bd762f3c3d9114938.png)
其中所有正确结论的序号是
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6卷引用:北京大学附属中学2022届高三三模数学试题
北京大学附属中学2022届高三三模数学试题(已下线)考向06 函数的奇偶性与周期性、对称性(重点)(已下线)专题13 导数及其应用北京卷专题10函数及其性质(填空题)北京卷专题11B指对幂函数北京卷专题12导数及其应用(选择填空题)
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解题方法
2 . 曲线
过点
的切线也是曲线
的切线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
___________ ;若此公切线恒在函数
的图象上方,则a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444c515d7d962c13ba251def136875d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8373794d772ec75ee1d82f5cb1ed7ac2.png)
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3 . 在处理多元不等式的最值时,我们常用构造切线的方法来求解.例如:曲线
在
处的切线方程为
,且
,若已知
,则
,取等条件为
,所以
的最小值为3.已知函数
,若数列
满足
,且
,则数列
的前10项和的最大值为___________ ;若数列
满足
,且
,则数列
的前100项和的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e212cdbfba6610bc55df2c1a737407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69bf4686e4b23ff0a14ebeef826baf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d95c90e96f834ecebf4c9e131302144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b50577c3072777214887bab40be8e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284a20f4ff113189c2b77ac503cbed57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fcb8fe389fc3f2f8c82e6ff04c89bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd96f537f7971ade6b3fb0a137cec62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9186b7e1edbc3a4a03828159dc78b9da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef2c68eca886c8f5543782b86e79ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f37c589447bba4e81b0fa9b7cd15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/730f650aa06ea3951441a726c44e2d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abdec06ffe44c0b96f0b3b90deaea8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473f0d6e8af69147d18ec37217df37be.png)
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5卷引用:河北省衡水市2022届高三二模数学试题
河北省衡水市2022届高三二模数学试题(已下线)第39练 导数的概念、意义及运算山西省朔州市怀仁市第一中学2023届高三三模数学试题(已下线)模块六 专题14 易错题目重组卷(山西卷)福建省2022届高三毕业班4月百校联合测评数学试题
4 . 在平面直线坐标系
中,设抛物线
:
的焦点为
,直线
:
与抛物线
交于点
,且点
在
轴上方,过点
作抛物线
的切线与抛物线
的准线交于点
,与
轴交于点
.给出下列四个结论:
①
的面积是
;
②点
的坐标是
;
③在
轴上存在点
使
;
④以
为直径的圆与
轴的负半轴交于点
,则
.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92020e8ae02f1b51d5c8d84e12bffa49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fb4c7a4bf45e467b2d90f6325056c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
②点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f47aca7742d68716383a31b72e7cc5.png)
③在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a3fdb2485d9b054a2821bae9a5626d.png)
④以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b95463a97c60db3250cb641bf6523d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63ae08af34db9433cb38ebc53e61349.png)
其中所有正确结论的序号是
您最近一年使用:0次
2022-03-30更新
|
1046次组卷
|
4卷引用:北京市朝阳区2022届高三一模数学试题
北京市朝阳区2022届高三一模数学试题(已下线)秘籍09 双曲线-备战2022年高考数学抢分秘籍(全国通用)(已下线)数学-2022年高考押题预测卷03(北京卷)北京卷专题12导数及其应用(选择填空题)
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5 . 过原点作曲线
的切线l,并与曲线
交于
,
两点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4b0017fdc3b97369ce3b2bd287fb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e76247c55f75c7afc092a9c6189264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a271c41a8bb40f52be1b5cede05902c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a86d65aab881fdd06a05ce47d09c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
您最近一年使用:0次
2023-03-22更新
|
457次组卷
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2卷引用:2022年新高考原创密卷数学试题(四)
2022·全国·模拟预测
6 . 已知定义在R上的函数
满足:①曲线
上任意一点处的切线斜率均不小于1;②曲线
在原点处的切线与圆
相切,请写出一个符合题意的函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed582a84139c6d541cf7478621151876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
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7 . 过点
作抛物线
的两条切线,切点分别为
,
,作
,
垂直于直线
,垂足分别为
,记
的面积分别为
,则
的最小值为____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732d1f2442a24cfa7276c6f6e0116afe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bde8a12369d468593dceb7d805ae578.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fe69909074860a8a0633867886b9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b862d01cd43ef85251c794a9f526ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718faf1812e063adeb6b527354b7ef2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f043837016a7457a528ee0d815b4ff7.png)
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8 . “S”型函数是统计分析、生态学、人工智能等领域常见的函数模型,其图象形似英文字母“S”,所以其图象也被称为“S”型曲线.某校生物兴趣小组在0.5毫升培养液中放入5个大草履虫,每隔一段时间统计一次大草履虫的数量,经过反复试验得到大草履虫的数量
(单位:个)与时间
(单位:小时)的关系近似为一个“S”型函数
.已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a59b0523303b7b84657d90fe956d0b.png)
.的部分图象如图所示,
为
的导函数.
①对任意
,存在
,使得
;
②对任意
,存在
,使得
;
③对任意
,存在
,使得
;
④对任意
,存在
,使得
.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ba27f55d572eae4b2369a9983a1ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a59b0523303b7b84657d90fe956d0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c81b29ac8a01886b25dcef55c5f6877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e01f1106983e1d6b46161e1213c65d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630a0b4b243ea5997de1b6cdf5653f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882e735e06541e2e6c542bc2af7f8fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace0286507d09fa10249582fdeeb4487.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630a0b4b243ea5997de1b6cdf5653f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882e735e06541e2e6c542bc2af7f8fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa658b7a15ce79949ece7485040d40e.png)
③对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882e735e06541e2e6c542bc2af7f8fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630a0b4b243ea5997de1b6cdf5653f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3180fc5e6ba0ecebabc90531288aa34b.png)
④对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882e735e06541e2e6c542bc2af7f8fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630a0b4b243ea5997de1b6cdf5653f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028f77357b896f66b64768e72151f098.png)
其中所有正确结论的序号是
您最近一年使用:0次
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|
1267次组卷
|
8卷引用:北京市朝阳区2021届高三下学期二模数学试题
北京市朝阳区2021届高三下学期二模数学试题(已下线)5.1导数的概念(B 能力培优练)-2021-2022学年高二数学同步双培优检测(苏教版2019选择性必修第一册)(已下线)2020年高考北京数学高考真题变式题11-15题北京一零一中学2023届高三下学期开学考数学试题北京卷专题12导数及其应用(选择填空题)北京市第一六六中学2023-2024学年高二下学期3月月考数学试题北京市海淀区北京一零一中2023-2024学年高二下学期期中考试数学试题(已下线)专题8 函数新定义问题【讲】(压轴题大全)
9 . 牛顿法求函数
零点的操作过程是:先在x轴找初始点
,然后作
在点
处切线,切线与x轴交于点
,再作
在点
处切线,切线与x轴交于点
,再作
在点
处切线,依次类推,直到求得满足精度的零点近似解为止.设函数
,初始点为
,若按上述过程操作,则所得前n个三角形
,
,……,
的面积和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37bb5bc3331eca0884620014e104b65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0472458c2169cfdae8c2f633b02f5972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/791532f9da2174275ef4643e4ab3f382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0fb5768a7a0765c8d959bd81fbae10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e62eff8a15c94222ebd1f57379d72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d16716eed20f9387ee72d51a15485c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5b8aed34b9a9ee3bd03e6e3c41e7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb54249d3a646e13cdb28455f9cd9d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174f269ebeda267b10df5b87e4b033b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2392f7f5646eb417eb5426d03008de.png)
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10 . 若两个函数
和
存在过点
的公切线,设切点坐标分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da03fbf994015e5a3a03de28734e0a1a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc91186336b2d99e88fe87e381c775c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028e90690c7cf3cd03405f2c7bc07122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7362fa526a84b0ce2f5a2021dbc44399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f455378328d1f31e18c413f327cb81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da03fbf994015e5a3a03de28734e0a1a.png)
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