题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-44174.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-66167.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-29483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-42456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-68369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-92984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-10307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-70944.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-16956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-11849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-57050.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-81156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-52104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-49884.png)
解析
试题分析:(I)∵
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181024-56932.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181024-23682.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181024-62527.png)
∴曲线
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-29483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181021-42456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181024-18780.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181024-38536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181025-85342.png)
则条件中三条直线所围成的三角形面积为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181025-63941.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-11849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-57050.png)
(II)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181025-56823.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181025-92525.png)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181025-33836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181026-34244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181026-56001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-49884.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181026-60809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181026-80571.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181027-43667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181026-56001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181027-60025.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181027-24745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181027-99834.png)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-81156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181022-65779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-52104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181023-49884.png)
点评:中档题,本题属于导数应用中的基本问题,通过求导数,确定得到切线的斜率,通过研究导数的正负,明确函数的单调性。本题函数式中含有参数a,需要运用分类讨论思想,增大了具体地难度。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181007-39857.png)
(1)证明函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181008-60177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181008-65675.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181008-15983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181009-70753.png)
(3)在(2)的条件下,若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181009-57321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181009-62248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181009-57792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181009-86502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181010-80361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181011-27693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181011-60670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819181011-32056.png)
(1)求f(x)和g(x)的解析式;
(2)若h(x)=f(x)-λg(x)在区间[-1,1]上是增函数,求实数λ的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180957-92636.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180957-78995.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180957-23673.png)
(2)解关于
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180957-58664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180958-61504.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180953-60237.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180953-98572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180954-79899.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180954-42813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180954-96603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180954-79899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180945-58685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180945-81305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180946-89526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180946-25105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819180946-24880.png)
A.0 | B.-14 | C.-9 | D.-3 |
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