题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-38828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-22199.gif)
⑴试求m、n的值;
⑵求过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-84583.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-42914.gif)
⑶过点A(1,t)是否存在与曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-42914.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-97140.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061221-52383.gif)
所以,-2和2为方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061221-81982.gif)
由韦达定理知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061221-87022.gif)
⑵∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061221-55881.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061221-98506.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061222-96361.gif)
当A为切点时,切线的斜率
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061222-37831.gif)
∴切线为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061222-67966.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061222-94386.gif)
当A不为切点时,设切点为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-17126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-25559.gif)
切线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-56821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-80440.gif)
因为过点A(1,-11),
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061224-15383.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061224-87791.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061224-38880.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061224-47101.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061224-76555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061224-47101.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061225-35572.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061225-64124.gif)
切线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061225-75202.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061225-55773.gif)
所以,过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061220-84583.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061222-94386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061225-55773.gif)
⑶存在满足条件的三条切线. …………10分
设点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-17126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061221-55881.gif)
则在P点处的切线的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-56821.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061223-80440.gif)
因为其过点A(1,t),所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061226-15009.gif)
由于有三条切线,所以方程应有3个实根, …………………………11分
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061226-81755.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061226-48814.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061226-72905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061226-20583.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061227-61014.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061227-57489.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061227-53497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061227-58154.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061228-99873.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061228-35480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061228-45177.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061227-53497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061228-55755.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061229-33987.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061229-41539.gif)
所以要使曲线与x轴有3个交
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061229-83586.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061229-91953.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061229-35925.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061230-90713.gif)
解析
核心考点
试题【已知函数的减区间是.⑴试求m、n的值;⑵求过点且与曲线相切的切线方程;⑶过点A(1,t)是否存在与曲线相切的3条切线,若存在求实数t的取值范围;若不存在,请说明】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061215-56733.gif)
A.![]() ![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061212-34059.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061212-34271.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061213-97857.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061213-39278.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061213-46841.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061213-72997.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061206-16938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061206-51577.gif)
A.![]() | B.![]() | C.![]() ![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061203-78180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061203-16379.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061154-80626.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061154-65260.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061154-95813.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061154-50978.gif)
(2)求证:当0<
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061154-11717.gif)
(3)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061154-27445.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061155-96902.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018061155-78113.gif)
最新试题
- 1下列说法正确的是( )A.由一种元素组成的物质叫做单质B.红磷在氧气中燃烧,产生大量白烟C.与水具有相同化学性质的最小
- 2阅读理解。 Mr Grey was the manager (经理) of a small office in
- 3有一瓶食用油用掉一半,则剩下的半瓶油[ ]A.密度为原来的一半 B.质量为原来的一半 C.体积、密度都为原来的一
- 4关于免疫的叙述,不正确的一项是( )A.免疫并不总是对人体有益的B.从定义上说,免疫就是指人体对病原体的抵抗力C.当人
- 5【题文】读下图,完成问题。【小题1】图中河流①②③段主要受到的河流作用依次是( )A.
- 6若(x+)n的展开式中前三项的系数成等差数列,则展开式中x4项的系数为A.6B.7C.8D.9
- 75.6克两种氧化物的固体混合物恰好与100克7.3%的盐酸完全反应,则该混合物可能是( )A.氧化镁和氧化锌B.氧化钙
- 8 — What’s the matter with John? He has been sitting there fo
- 9为下列词语中划线的字注音。 酝酿( ) 镶( )边 唱和( ) 枯涸( )
- 10若x1、x2是一元二次方程2x2-3x-1=0的两个根,求下列代数式的值.(1)1x1+1x2(2)x12+x22(3)
热门考点
- 1若函数的定义域为R,则实数可的取值范围是___________.
- 2鸟类足的形态与它的生活环境相适应.如图所示是几种鸟类的足,其中为野鸭的是( )A.B.C.D.
- 3补写出下列名篇名句中的空缺部分。(6分)小题1:出师未捷身先死, 。(杜甫《蜀相》)小题2:夫祸患常积于忽微,
- 4下列各组词语,有错别字的一项是[ ]A、钩连 潦倒 地崩山摧 群山万壑 B、峥嵘 谪居 冲波逆折 篮
- 5下列文件中,明确提出要解除对于英国国王的一切隶属关系,要求民族独立的是A.《权利法案》B.《独立宣言》C.《人权宣言》D
- 6一个由电阻均匀的导线绕制成的闭合线圈放在磁场中,如图所示,线圈平面与磁场方向成60°角,磁感应强度随时间均匀变化,下列方
- 7如图的各省级行政区中,位于我国北方地区的是( )A.①②③④B.①②④C.②③④D.②④
- 8阅读文段,回答问题。雨的四季刘湛秋 我喜欢雨,无论什么季节的雨,我都喜欢。她给我的形象和记忆,永远是美的。 春天,树
- 9某日中午,北方某地气温由早晨的零下2℃上升了9℃,傍晚又下降了3℃,这天傍晚北方某地的气温是( )℃。
- 10如图所示,电灯L标有“4V,1W”,滑动变阻器R总电阻为50Ω,当滑片P滑至某位置时,L恰好正常发光,此时电流表示数为0