1 . 已知函数
.
(1)当
时,若直线
与曲线
相切,求
;
(2)若直线
与曲线
恰有两个公共点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db6dc5779e96494ef7f1c8f973ea86b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634cfbfa72c819314962cc08fc29ac15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f590ca2bde213675bffe68ed4017f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2 . 下列导数运算正确的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 求下列函数的导数.
(1)①
;②
;③
;
(2)①
;②
;
(3)①
;②
;③
.
(1)①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884e534313d810d5fc36b95f9fcaa08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e769299acbcc266a35ddd6848452f14.png)
(2)①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11b587eab7ca8cd4ec6d3dd1c8b4585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10408555b8279a4e9621d077acf7a97.png)
(3)①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125bea9ef0d4a26ac65cacf66536b388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1454530ed83e70e2831ec0fd8d9d48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e841547b8732a15323ab74fb109f360.png)
您最近一年使用:0次
4 . 曲线
在点
处的切线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd9c33bde28a4f5e3d085d60e71d33b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d66e9d52546beeea016d6d7d3f0ca6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
5 . 已知
,则曲线
在点
处的切线斜率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34206a83c04f3d6a64f51800fc83d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6715d5b63d9470c6e6980940141da0.png)
您最近一年使用:0次
昨日更新
|
128次组卷
|
2卷引用:陕西省咸阳市实验中学2023-2024学年高二下学期第三次月考数学试题
名校
解题方法
6 . 已知函数
及其导函数
的定义域均为
,记
.若
与
均为偶函数,且
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d6fa911e3396b34fb470c10b063fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1aa50ff3aa2aa872bc41acaab8787b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb1755255a99ef00869962bb8e745ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7326ef4ba9ace3e76f3c17370a2d8e.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
昨日更新
|
708次组卷
|
4卷引用:黑龙江省哈尔滨市第六中学校2024届(2021级)高三下学期四模数学试题
黑龙江省哈尔滨市第六中学校2024届(2021级)高三下学期四模数学试题 (已下线)模型5 函数性质的综合运用模型(已下线)第13题 原函数与导函数的图像、性质联系问题(高二期末每日一题)河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
7 . 如果方程
能确定
是
的函数,那么称这种方式表示的函数为隐函数.隐函数的求导方法如下:在方程
中,把
看成
的函数
,则方程可看成关于
的恒等式
,在等式两边同时对
求导,然后解出
即可.例如,求由方程
所确定的隐函数的导数
,将方程
的两边同时对
求导,则有
(
是
的函数,需要用复合函数的求导法则求导),得
.利用隐函数求导方法可求得曲线
在点
处的切线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbbf52d1f9d61b41bdd4acfc9fac268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbbf52d1f9d61b41bdd4acfc9fac268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d318c5ba5c7154bbcc95f8ec8e3d4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fe744d4980ba5e09c4074e0643e635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e70497c791fd23d1f37a544f2f73f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9bf4c61dd281154e8cc5771a5f6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9bf4c61dd281154e8cc5771a5f6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3731ec916f7866d93c5d22f7f70f202f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e696074c13fecc9bf8853d65c3776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b3b2e2820c19241b0e5770445f1d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知函数
为奇函数,其图象在点
处的切线方程为
,记
的导函数为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b76ab35fb2b82bb645aea1e3dcdfd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04eed461026f69fe9ab2c5dc12af8ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce355157e6f86449245ab7958edf1aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9363ef93a1d0d413de1d9d5b84da8.png)
A.2 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
9 . 小明研究函数
的图象与导函数,经查阅资料,发现
具有下面的性质:若函数
在
上的导函数为
,且
在
上也存在导函数,则称函数
在
上存在二阶导函数,简记为
.若在区间
上
,则称函数
在区间
上为“凹函数”.请你根据以上信息和所学知识,判断以下函数在其定义域上是“凹函数”的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affdb4e0e91ead05b2684c52f341d935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0dd6144e9a30d1a063b690033c3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 求满足下列条件的直线
的方程.
(1)
为曲线
在
处的切线;
(2)
的斜率为
且与曲线
相切;
(3)
过原点且与曲线
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8514119ac8a6ad109fd7b468894a3f26.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
您最近一年使用:0次