题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055755-34013.gif)
(1)当t=1时,求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055755-41179.gif)
(2)当t≠0时,求的单调区间;
(3)证明:对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-36702.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-47343.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-41858.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-36647.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-99284.gif)
因为t≠0,以下分两种情况讨论:
①若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-41895.gif)
x | ![]() | ![]() | (-t,∞) |
![]() | + | - | + |
![]() | ![]() | ![]() | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-43657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-50380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055757-69468.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-43657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-29332.gif)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055757-71023.gif)
x | (-∞,t) | ![]() | ![]() |
![]() | + | - | + |
![]() | ![]() | ![]() | ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-43657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055757-96868.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-43657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055757-13060.gif)
(3)由(2)可知,当t>0时,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-43657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055758-47913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055757-96868.gif)
以下分两种情况讨论:
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055758-18877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055758-97679.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055758-11302.gif)
所以对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055759-41343.gif)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055759-73653.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055756-43657.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055758-47913.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055759-22859.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055759-40251.gif)
解析
核心考点
试题【(14分)已知函数,(1)当t=1时,求曲线处的切线方程;(2)当t≠0时,求的单调区间;(3)证明:对任意的在区间(0,1)内均存在零点。】;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/20191018/20191018055745-16584.gif)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055745-61357.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055745-30580.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055745-65252.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055746-71739.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055746-72502.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055731-20169.gif)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055731-36427.gif)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055731-36427.gif)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055732-44217.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055732-97294.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055732-41862.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055732-19923.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055732-89405.gif)
已知二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-56646.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-68262.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-52901.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-99046.jpg)
(
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-45473.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-52901.gif)
(2)记
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-18845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055723-12722.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055724-80618.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055724-83447.gif)
已知f(x)=lnx+x2-bx.
(1)若函数f(x)在其定义域内是增函数,求b的取值范围;
(2)当b=-1时,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055716-80975.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055704-80423.gif)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-59623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-40516.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-76810.gif)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-59623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-29877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055706-53641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-29877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-59623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055706-30120.gif)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055706-85315.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055706-80356.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-29877.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055705-59623.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055706-80356.gif)
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