题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042306-84694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042306-30105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-66613.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-35275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-15601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-57947.png)
(2)在(1)的结论下,设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-93735.png)
(3)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-92121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-37813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-89783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-91614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-62128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-67120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-13305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-37813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-90773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-60565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-67120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-37813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-90773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-60565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-67120.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-97080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-17450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-99901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-25267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-34056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-99901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-65549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-38220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-99901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-75828.png)
解析
试题分析:本题主要考查导数的运算,利用导数研究函数的单调性、不等式基础知识,考查函数思想、构造函数思想、分类讨论思想,考查综合分析和解决问题的能力.第一问,利用导数研究函数的单调性,转化为恒成立问题,再转化为求函数最值问题;第二问,利用配方法求最值,讨论对称轴与区间端点的大小,本问突出体现了分类讨论思想的运用;第三问,把问题坐标化,用反证法证明,利用切线平行,列出方程,构造函数,判断单调性求最值,得出矛盾.
试题解析:(1)依题意:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-59284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-79291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-39971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042312-57209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042312-49434.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042312-37580.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042312-41903.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042312-69540.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042307-57947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042309-97080.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042312-94193.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-67179.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-75141.png)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-52141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-17450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-60914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-67263.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042314-79954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042314-50697.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042314-27280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-34056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042314-71569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042314-12825.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042315-84401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-38220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-60914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042313-67263.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042315-74874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042315-93599.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-17450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-99901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-25267.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-34056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-99901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-65549.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-38220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042310-99901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042311-75828.png)
(3)设点
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-91614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042315-44967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042315-71955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-11049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-44868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-37813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-87222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-35106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-10418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042317-25442.png)
假设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-37813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-87222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042308-60017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042316-10418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042317-10934.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042317-59702.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042317-94733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042317-40906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042318-16912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042318-44168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042318-68486.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042318-48816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042318-13708.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042318-62680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042319-15995.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042319-78850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042319-14821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042319-66909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042319-46113.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042320-84776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042320-17607.png)
这与①矛盾,假设不成立.故C1在点M处的切线与C2在点N处的切线不平行. 14分
核心考点
试题【已知函数, .(1)若, 函数 在其定义域是增函数,求的取值范围;(2)在(1)的结论下,设函数的最小值;(3)设函数的图象与函数的图象交于点,过线段的中点作轴】;主要考察你对函数的单调性与最值等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042256-65790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042256-87604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-42780.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-11426.png)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-27544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-51675.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-42780.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-71702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042257-73759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042258-32971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042258-10498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042252-93662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042252-70098.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042253-18018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042253-86077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042253-91950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042253-26450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042252-70098.png)
A.有最小值0,无最大值 | B.有最小值-1,无最大值 |
C.有最大值1,无最小值 | D.无最大值,也无最小值 |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042245-84834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042246-72035.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042246-50437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042246-72035.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042246-50437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042228-59843.png)
(1)在区间
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042228-92282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042228-74946.png)
(2)设集合
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042228-33940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042229-54946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042229-22251.png)
的关系,并给出证明 ;
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042229-77226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042229-71443.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042230-26546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042228-74946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818042230-93265.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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