题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132408-20929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132408-42936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132408-81945.png)
(1) 将函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132408-15033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-45197.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-45197.png)
(2) 关于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-94332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-50831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-90283.png)
(3)对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-20212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-43240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-94332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-45561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-11244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132411-17137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132411-13553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-20212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-43240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132411-83866.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132411-20961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-20212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-43240.png)
答案
解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-86678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-96572.png)
(2)解法一:不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132409-50831.png)
等价于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-79220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-91278.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-16221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132413-56019.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132413-56276.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-16221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132413-89878.png)
则另一个零点一定在区间
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132413-29919.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132414-15967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132414-23803.png)
解法二:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-79220.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132412-91278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132414-53195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132414-51018.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132415-11077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132415-82312.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132415-61947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132414-23803.png)
(3)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132415-44014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132415-64258.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132416-66980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132416-79211.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132416-58590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132416-17812.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-69494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-68802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-51053.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-20212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-43240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-69494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-15056.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-20212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132410-43240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132418-70047.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132418-58190.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132418-18609.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132418-53913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132419-69151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132418-53913.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132419-95288.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132419-50485.png)
下面证明
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132419-48372.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132420-86567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132420-56707.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132416-66980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132420-94391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132416-58590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132420-42843.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-69494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132420-46586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132417-51053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132421-24311.png)
故所求“分界线”方程为:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132421-48811.png)
解析
核心考点
试题【(本题满分12分) 设函数(),.(1) 将函数图象向右平移一个单位即可得到函数的图象,试写出的解析式及值域;(2) 关于的不等式的解集中的整数恰有3个,求实数】;主要考察你对函数的单调性与导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132016-95512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132017-65983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132017-85693.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132017-26976.png)
(Ⅱ)函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132017-47208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132018-74200.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132018-75206.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018132018-77177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131820-71676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131820-76517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131820-42877.png)
A.![]() | B.![]() | C.![]() | D.![]() |
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131805-29507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131805-96764.png)
(I)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131806-19382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131806-16616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131806-18958.png)
(II)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131807-90782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131807-18196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131805-29507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131807-38494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131807-91805.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131738-38923.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131739-77064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131739-88562.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131739-44295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131740-76261.png)
(Ⅲ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131740-62272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131740-90666.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131740-23079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131740-56467.png)
使
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131741-90519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131741-92314.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131741-46986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131742-28225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131716-52327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131716-63442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131716-92774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131716-57586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018131717-53816.png)
(1)当p是真命题,求m的取值范围;
(2)当“p或q”为真命题,“p且q”为假命题时,求m的取值范围。
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