题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133506-61335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133506-29225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133506-42274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133506-25000.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133507-47550.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133507-93678.png)
(2)证明:曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133507-47550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133507-93678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133507-52688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133507-68149.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133508-60182.png)
解析
试题分析:(1)解 f′(x)=a-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133508-38404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133508-47838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133508-51367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133509-94554.png)
因为a,b∈Z,故f(x)=x+
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133508-60182.png)
(2)证明 在曲线上任取一点(x0,x0+
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133509-89050.png)
由f′(x0)=1-
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133509-14036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133509-94121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133509-71248.png)
令x=1,得y=
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133510-41530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133510-90358.png)
令y=x,得y=2x0-1,切线与直线y=x的交点为(2x0-1,2x0-1);
直线x=1与直线y=x的交点为(1,1),从而所围三角形的面积为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133511-96500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133511-70049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133511-96500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133511-18706.png)
点评:主要是考查了导数的几何意义求解切线方程,以及三角形的面积,属于基础题。
核心考点
试题【设函数(,b∈Z),曲线在点(2,)处的切线方程为=3.(1)求的解析式;(2)证明:曲线=上任一点的切线与直线和直线所围三角形的面积为定值,并求出此定值.】;主要考察你对导数的意义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133451-11130.png)
(I)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133451-50892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133451-21083.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133452-76867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133452-57026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133452-38612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133452-25916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133452-10250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133453-51128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133447-31352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133447-78540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133439-26701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133439-20946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133439-48693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133440-79276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133440-23106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133440-20265.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133433-23582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133434-57756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133434-82282.png)
A.-3 | B.9 | C.-15 | D.-7 |
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133428-49869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017133429-61215.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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