题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-60342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-38376.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
(2)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-47307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-97211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-47307.png)
在,说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-41292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-97542.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-65915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-31063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-74669.png)
解析
试题分析:(1)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-36805.png)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-74374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140538-90647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140538-61768.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140538-27704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140538-46040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140539-31716.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140539-95731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140539-97401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140539-98844.png)
(ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140540-79517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140540-82556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140540-44100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140540-10079.png)
∴ 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
(ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140541-93617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140541-64766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140539-97401.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140541-15704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140541-28773.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140541-37513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140542-95983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140542-79115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140542-65889.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-41292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140542-26673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140543-26422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140542-65889.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140543-63101.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140543-57965.png)
∴函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140543-23965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-65915.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-41292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-97542.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-65915.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-31063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
(2)由(1)得当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-31063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-41292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-97542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-65915.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-30689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140543-29017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140541-28773.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140544-79028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140544-13867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140544-93686.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140544-15834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140544-78241.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140545-84333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-89902.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140545-67602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140545-95946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140546-30374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140546-89319.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140546-91677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140546-27775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140546-88164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140546-30374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140547-71195.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140547-10331.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140536-41292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140547-32264.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140535-47307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140537-74669.png)
点评:本题考查利用导数研究函数的单调性,利用导数研究函数的极值,突出分类讨论思想与转化思想的渗透与应用,属于难题,第二题把有正的极大值的问题转化为图象开口向下与X轴有两个交点,思路巧妙,学习中值得借鉴.
核心考点
举一反三
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140531-76690.png)
(I)若曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140531-54759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140531-54523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140531-59684.png)
(II)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140532-38693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140507-11485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140508-83089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140508-13399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140508-24284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140508-53770.png)
(Ⅰ) 求
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140509-19743.png)
(Ⅱ) 求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140509-54752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140501-26623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140502-54885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140443-70426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140443-70648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-58672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-79928.png)
(Ⅰ) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-58672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-79928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-79928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-48307.png)
(Ⅱ) 若
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-24712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140444-48307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191017/20191017140434-32116.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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