名校
1 . 极值的广义定义如下:如果一个函数在一点的一个邻域(包含该点的开区间)内处处都有确定的值,而以该点处的值为最大(小),这函数在该点处的值就是一个极大(小)值.
对于函数
,设自变量x从
变化到
,当
,
是一个确定的值,则称函数
在点
处右可导;当
,
是一个确定的值,则称函数
在点
处左可导.当函数
在点
处既右可导也左可导且导数值相等,则称函数
在点
处可导.
(1)请举出一个例子,说明该函数在某点处不可导,但是该点是该函数的极值点;
(2)已知函数
.
(ⅰ)求函数
在
处的切线方程;
(ⅱ)若
为
的极小值点,求a的取值范围.
对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47db6b322f19cefcd70d0f8433917f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1459527045d2d138d1ee4b441aade53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e6c43466d743ea37287656b85821c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570e972f51cd1d11acfd80a01c0512fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e6c43466d743ea37287656b85821c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(1)请举出一个例子,说明该函数在某点处不可导,但是该点是该函数的极值点;
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae34b02b147bb49131a01316e07efaf.png)
(ⅰ)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1735755a0f13e329df682712dd1d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2 . 第二十五届中国国际高新技术成果交易会(简称“高交会”)在深圳闭幕.会展展出了国产全球首架电动垂直起降载人飞碟.观察它的外观造型,我们会被其优美的曲线折服.现代产品外观特别讲究线条感,为此我们需要刻画曲线的弯曲程度.考察如图所示的光滑曲线
上的曲线段
,其弧长为
,当动点从
沿曲线段
运动到
点时,
点的切线
也随着转动到
点的切线
,记这两条切线之间的夹角为
(它等于
的倾斜角与
的倾斜角之差).显然,当弧长固定时,夹角越大,曲线的弯曲程度就越大;当夹角固定时,弧长越小则弯曲程度越大,因此可以定义
为曲线段
的平均曲率;显然当
越接近
,即
越小,
就越能精确刻画曲线
在点
处的弯曲程度,因此定义
(若极限存在)为曲线
在点
处的曲率.(其中
,
分别表示
在点
处的一阶、二阶导数)
的焦点到准线的距离为3,则在该抛物线上点
处的曲率是多少?
(2)若函数
,不等式
对于
恒成立,求
的取值范围;
(3)若动点
的切线沿曲线
运动至点
处的切线,点
的切线与
轴的交点为
.若
,
,
是数列
的前
项和,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d0dd437ad522066cc7d4b7d208e2866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427eceadd7bb569ff140ea73d650db1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952bd235a906f77d227dfcfe1cbea780.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.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/0e313d2b28b6d3d6273346e8f9bb78c9.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/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b6c6aec8cfad1ce0277d6db9759c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ad52c0008b852946f7e316474e396d.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd589f01fd5de86d37e197e022f9dc36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692a685d89c02da9bab03b7adbd66adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aedc1c8a16e306bcd6e5154f9ed6dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(3)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d637a9d76ce3058a0e9b561c832d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cac935140541b5e1ba7d7dfffdd8325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3cbcc09d6f5004f2509aad50eef40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e858cf44005397a29962fda98a020d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819480e1e624208f729ad8653e4f24f.png)
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名校
3 . 若曲线C的切线l与曲线C共有n个公共点(其中
,
),则称l为曲线C的“
”.
(1)若曲线
在点
处的切线为
,另一个公共点的坐标为
,求
的值;
(2)求曲线
所有
的方程;
(3)设
,是否存在
,使得曲线
在点
处的切线为
?若存在,探究满足条件的t的个数,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a4e961d362e7454658bad29750a1cd.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567c7a1edad2de8d71a06eb76c8b52b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad42625f296d2a4b65180e2f7b776beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680c514271ab4a9c8424873bd5e2b154.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d395a5e66576b31ba39a2abcecc26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a442bb3027296d45df4b72609b5d02.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d71f56ef6906bc37ca312051d97d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce71911f990a0d69b54c6ca453ac9a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56849f3da518eff9bf32c7149f9d49b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0520cf6db4ec82dc0e092f2aa0036427.png)
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名校
4 . 已知函数
.
(1)若过点
可作曲线
两条切线,求
的取值范围;
(2)若
有两个不同极值点
.
①求
的取值范围;
②当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30e674c62fd9e25645b3984827759a6.png)
(1)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e868d1326bf73ac658885d4936bbe04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7913a814e2c4ba5e643af885b6ff0efb.png)
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2024-06-11更新
|
616次组卷
|
4卷引用:专题7 导数与极值点偏移【练】
解题方法
5 . 已知曲线
在点
处的切线方程为
.
(1)求a,b的值;
(2)求
的单调区间;
(3)已知
,且
,证明:对任意的
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a274b0623171972513340511781ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2e4560759a110e4ccc334e3ccea7e4.png)
(1)求a,b的值;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9c008f8fcc8edcd68fb14e0727fa49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bccf433ec08ad06d0e8a7eb53f5143ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6de235c7c5205eb3d81109f04abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e176b379350d3bbdbb923c2e8435f011.png)
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2024高三·全国·专题练习
解题方法
6 . 已知函数
,
.
(1)若直线
是函数
的图象的切线,求实数
的值;
(2)当
时,证明:对于任意的
,不等式
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4148eb89c1d500c7de387547772f888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1495821fad209346487928e0429f742.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa204d6b5183969f6da37f369eb7293d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868ee58bffacef0b08d55d53dbe6f8f8.png)
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7 . 若函数
在
上有定义,且对于任意不同的
,都有
,则称
为
上的“k类函数”.已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求
的单调区间;
(3)若
为
上的“3类函数”,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d6fe21d6ed78bfc1d2b9cc41a766c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeaea651d833a0fd5a2a7f0cbaeb4ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485825faa883e045117e914fc4094908.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
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8 . 已知函数
,若数列
的各项由以下算法得到:
①任取
(其中
),并令正整数
;
②求函数
图象在
处的切线在
轴上的截距
;
③判断
是否成立,若成立,执行第④步;若不成立,跳至第⑤步;
④令
,返回第②步;
⑤结束算法,确定数列
的项依次为
.
根据以上信息回答下列问题:
(1)求证:
;
(2)是否存在实数
使得
为等差数列,若存在,求出数列
的项数
;若不存在,请说明理由.参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71601a0573a3d598bea17f989570fd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
①任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd3ecf27b4de4d36c92c072b17a2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
②求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d896b1e6cadb21a23acb227c18b238b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
③判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11ef454b69c4ce4fd731b6f2ec13d70.png)
④令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2583433b021057d8bf772e20f9420a.png)
⑤结束算法,确定数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a94ba3f4906ba526f9f6676540a99b6.png)
根据以上信息回答下列问题:
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bedf7ef340c4cb9522106f53ef5f37.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb6e83865e833f866807dfbced86dc9.png)
您最近一年使用:0次
9 . 已知函数
.
(1)求函数
的单调区间;
(2)若函数
在
处取得极大值,求实数
的取值范围:
(3)已知
,曲线
在不同的三点
处的切线都经过点
,且
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50bdf9cc570f3ad7245aca7087abe6b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a54f63ff36b084047321e09cbcee442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606ef9cb8c9c4f61ab2acc4c11fec693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5149c72ec2f361d9220b6bf8bba4dc3.png)
您最近一年使用:0次
名校
10 . 已知直线
与曲线
相交于不同两点
,曲线
在点
处的切线与在点
处的切线相交于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.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/7775aa57ca0e62216f3039ed88dceed0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次