1 . 已知函数
,
.
(1)若直线
为曲线
的一条切线,求出b与k的函数关系式;
(2)当
时,过点
的
的切线l也与曲线
相切,试求直线l的条数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81172737954597d9945d1e7ef7f8870e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32cd98d2758c059d11de353ccbad27fa.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e34f42b3be15518c29e3689c9fe6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e32be4e76999e41eb70f75d164a6278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069c50175f97527ad7b7bc31c5f87d5.png)
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2 . 判断下列命题正确的是( )
A.函数的极大值一定比极小值大 |
B.对于可导函数![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.一元三次函数在![]() |
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3 . 已知
是
的导函数,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba0cdf216c7ff5b80f2f43cb3470117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图,已知椭圆
(
)的左,右顶点分别为
,
,椭圆的长轴长为4,椭圆上的点到焦点的最大距离为
,
为坐标原点.
的方程;
(2)设过点
的直线
,
与椭圆分别交于点
,
,其中
,
①证明:直线
过定点,并求出定点坐标;
②求
面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](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/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e511d8ecf566c5c0730bbe6be0d6347c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800c5e266b4ad8462a46970f0a232d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46b053f98b1d05a2043e94eeaefea87.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/58b140e221ddf537b8964fff8557cca0.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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5 . 已知函数
.
(1)证明:
恰有一个零点
,且
;
(2)我们曾学习过“二分法”求函数零点的近似值,另一种常用的求零点近似值的方法是“牛顿切线法”.任取
,实施如下步骤:在点
处作
的切线,交
轴于点
:在点
处作
的切线,交
轴于点
;一直继续下去,可以得到一个数列
,它的各项是
不同精确度的零点近似值.
(i)设
,求
的解析式;
(ii)证明:当
,总有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3904b79fdb74189b8b9933fdb6b341.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033efeaceca52396fa7eedd33f518162.png)
(2)我们曾学习过“二分法”求函数零点的近似值,另一种常用的求零点近似值的方法是“牛顿切线法”.任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9484dfcc25776aaf03bd76d2bdddb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb652143b43cc9439a347b2b1dc5cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc47735cc385a3474bc1dabad322304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367304824e7eb354ffeb937fa209d80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(i)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c0a98e6d574ec3702340e64bba6c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091f2176a35c27ac4bdddcda85de5bcc.png)
(ii)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9484dfcc25776aaf03bd76d2bdddb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a415b86943618bf0c8ebc5951a1aef.png)
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6 . 已知函数
,且
为极值点.
(1)求实数
的值;
(2)判断
是极大值点还是极小值点,并分别求出极大值与极小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf01bea8f990d27cf68303638b982cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde84fe5599f954da211908c42d3b63.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde84fe5599f954da211908c42d3b63.png)
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湖北省孝感方子高级中学2023-2024学年高二下学期3月月考数学试题 山西省2023-2024学年高二上学期1月期末质量检测数学试题(已下线)6.2.2 导数与函数的极值、最值(2知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)北京市陈经纶中学2023-2024学年高二下学期4月期中诊断数学试卷山西省朔州市怀仁市大地学校高中部2023-2024学年高二下学期第四次月考(6月)数学试题青海省海东市第一中学2023-2024学年高二下学期第一次月考数学试题(已下线)专题01 一元函数的导数及其应用-3
7 . 已知函数
,若
,则下列式子大小关系正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48973c97627421e4b0af05ddd40abd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2905ef7674574749b4ca9dd9cfe58cd.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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湖北省孝感方子高级中学2023-2024学年高二下学期3月月考数学试题 山西省2023-2024学年高二上学期1月期末质量检测数学试题(已下线)专题04导数期末10种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(人教B版2019选择性必修第三册)青海省海东市第一中学2023-2024学年高二下学期第一次月考数学试题
8 . 已知双曲线C:
,(
),的左、右焦点分别为
,
,双曲线C上两点A,B关于坐标原点对称,点P为双曲线
右支上一动点,记直线
,
的斜率分别为
,
,若
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d79a9d7c59c061259eba07baded4941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9626bd07f966ea26a51dcd8ceba04ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf32f4d595c02a8c0f7cc5f8fd0c931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bc8a1c303ee2b1588fd3e93968cd43.png)
A.![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.以![]() ![]() |
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9 . 动点G到点
的距离比到直线
的距离小2.
(1)求G的轨迹的方程;
(2)设动点G的轨迹为曲线C,过点F作斜率为
,
的两条直线分别交C于M,N两点和P,Q两点,其中
.设线段
和
的中点分别为A,B,过点F作
,垂足为D,试问:是否存在定点T,使得线段
的长度为定值.若存在,求出点T的坐标及定值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1bed885fcb17bdcc978ed955677f2b.png)
(1)求G的轨迹的方程;
(2)设动点G的轨迹为曲线C,过点F作斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae3ab048431fdc75f9a2eef2a762f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33daacca5f6f6681b662295ebb98587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1ab6c10bc0a8bfbdc3b4824c2de1d1.png)
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解题方法
10 . 已知抛物线
的焦点为F,若
的三个顶点都在抛物线E上,且满足
,则称该三角形为“核心三角形”.
(1)设“核心三角形
”的一边
所在直线的斜率为2,求直线
的方程;
(2)已知
是“核心三角形”,证明:
三个顶点的横坐标都小于2.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f4fb72e39d79b7a0cd892fa5fa34bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d856ed2306a7cc3e64a1edfb84627aa5.png)
(1)设“核心三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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