题目
题型:不详难度:来源:
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060430-19546.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060431-81319.gif)
⑴试求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060431-38468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060431-83784.gif)
⑵求过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060431-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060432-54253.gif)
⑶过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060432-85136.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060432-54253.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060432-87474.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060432-18236.gif)
所以,-2和2为方程
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060432-72361.gif)
由韦达定理知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060433-14225.gif)
⑵∵
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060433-70495.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060433-95666.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060433-76085.gif)
当A为切点时,切线的斜率
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060433-92150.gif)
∴切线为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060434-46922.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060434-56817.gif)
当A不为切点时,设切点为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060434-51210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060434-16825.gif)
切线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-57457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-44047.gif)
因为过点A(1,-11),
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-40747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-12477.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-16906.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060436-76982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060436-51029.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060436-76982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060436-43404.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060436-67202.gif)
切线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060437-86070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060437-90009.gif)
所以,过点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060431-74982.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060434-56817.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060437-90009.gif)
⑶存在满足条件的三条切线.
设点
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060434-51210.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060433-70495.gif)
则在P点处的切线的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-57457.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060435-44047.gif)
因为其过点A(1,t),所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060437-74873.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/20191018/20191018060437-95617.gif)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060438-71328.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060438-13342.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060438-79401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060438-46310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060438-57595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060439-64537.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060439-33785.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060439-65831.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060439-36899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060438-57595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060439-38010.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060440-36327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060440-32566.gif)
所以要使曲线与x轴有3个交点,当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060440-14096.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060440-28477.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060441-69488.gif)
解析
核心考点
试题【(本小题满分14分)已知函数的减区间是.⑴试求、的值;⑵求过点且与曲线相切的切线方程;⑶过点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,】;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/20191018/20191018060424-12178.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060424-94515.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060424-92513.gif)
(1)求m与n的关系表达式。(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060425-62357.gif)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060425-84000.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060425-34038.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060416-16828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060416-58344.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060416-97311.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060417-22246.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060417-25925.gif)
曲线y=
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060416-16828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060417-58123.gif)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060416-16828.gif)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060416-16828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060409-52550.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060403-35010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060403-22935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060403-30864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060403-37849.png)
和为( )
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060355-16631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018060355-37776.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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