题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-32034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-91409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-60698.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-91409.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-34357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-59092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-28644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-69898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-59092.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-98890.png)
(2)存在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-59092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-11420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-49628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-88384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-56011.png)
解析
试题分析:解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-95245.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-91409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-60698.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-60698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-41549.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020723-18218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020723-86541.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-98890.png)
(2)由题意知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020723-51139.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020723-34180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-95207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-60698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020723-76033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-69898.png)
![]() | ![]() | 1 | (1,3) | 3 | ![]() |
![]() | - | 0 | + | 0 | - |
![]() | 递减 | 极小值 | 递增 | 极大值 | 递减 |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020724-44030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020724-25358.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-56011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020725-54055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-56011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020725-88580.png)
因此,为使曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-88384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-56011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020724-44030.png)
得:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020725-60787.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-11420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-49628.png)
即存在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020720-59092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-11420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020721-49628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-88384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020722-56011.png)
点评:根据导数的符号判定函数的单调性是解题的关键,同时能利用其极值于x轴的关系的求解交点问题,属于中档题。
核心考点
试题【已知函数,且在和处取得极值.(1)求函数的解析式.(2)设函数,是否存在实数,使得曲线与轴有两个交点,若存在,求出的值;若不存在,请说明理由.】;主要考察你对函数极值与最值等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020714-45492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020714-63811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020714-69824.png)
求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020714-14822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020714-17972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020706-23050.png)
(Ⅰ)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020706-54641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020706-51599.png)
(Ⅱ)若存在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020706-39940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020707-52089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020707-80621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020706-54641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020707-21289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020652-65162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020653-69315.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020653-95615.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020653-16719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020653-29780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020653-72330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020647-33948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020647-28643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020648-72289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020648-24274.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020648-93543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020647-33948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019020648-30044.png)
A.4 | B.3 | C.8 | D.2 |
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