题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193739-22467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193739-20419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193740-68775.png)
(Ⅰ)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193740-53765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193740-26336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193740-26681.png)
(Ⅱ)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-21689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-91296.png)
(Ⅲ)对(Ⅱ)中的
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-91296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193742-52403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193742-96283.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193742-47170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-32146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-70637.png)
解析
试题分析:(Ⅰ)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-10719.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-57329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193744-29747.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193744-27272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193744-88556.png)
由已知得
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193745-70696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193742-47170.png)
∴两条曲线交点的坐标为(e2,e) 切线的斜率为k=f’(e2)=
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-32146.png)
∴切线的方程为 y-e=
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-32146.png)
(II)由条件知h(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193745-86895.png)
(i)当a>0时,令
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-74234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-77745.png)
∴当0 <
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-42703.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-12157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193747-76045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-12157.png)
当x>
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-12157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193747-34087.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193748-25271.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193746-77745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193748-62598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
∴最小值
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193748-83356.png)
(ii)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193748-13626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-75066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193741-37857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193743-70637.png)
(Ⅲ)由(Ⅱ)知
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-72402.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193750-28831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193750-20112.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193750-89084.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193750-40520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193751-47969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193751-80380.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193751-82924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193752-44253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193752-27551.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193750-89084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193753-15071.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-93776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193748-62598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193753-14890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193749-93776.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193742-52403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193753-28270.png)
点评:导数本身是个解决问题的工具,是高考必考内容之一,高考往往结合函数甚至是实际问题考查导数的应用,求单调、最值、完成证明等,请注意归纳常规方法和常见注意点
核心考点
试题【已知函数,,(Ⅰ)若曲线与曲线相交,且在交点处有相同的切线,求的值及该切线的方程;(Ⅱ)设函数,当存在最小值时,求其最小值的解析式;(Ⅲ)对(Ⅱ)中的,证明:当】;主要考察你对函数的相关概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193701-20293.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193701-77299.png)
A.(-![]() ![]() | B.(-![]() ![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193653-72034.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193653-93113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193602-65438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193602-37017.png)
A.-8 | B.-3 | C.3 | D.8 |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193512-23769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193513-30116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193513-22603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193513-89314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193513-22603.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193514-41565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193512-23769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193512-23769.png)
A.![]() ![]() |
B.![]() |
C.![]() ![]() ![]() |
D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193441-49391.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193442-62714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193442-62883.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193442-50366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193442-62883.png)
(Ⅲ)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193442-72717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193444-71379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193444-86212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200204/20200204193444-92198.png)
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