1 . 设函数
(
).
(1)讨论
的单调性;
(2)如果
有两个极值点
和
,我们记过点
的直线斜率为
.问:是否存在
,使得
?若存在,求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff4255bff210170362868e710db87ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450669619f798d4e05e3f67f72f34282.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0de3129f0c484d2542e4d0810cbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b680c9cf0ac2e7aed2f445597eb47446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-01-28更新
|
686次组卷
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2卷引用:2018年全国高中数学联赛甘肃省预赛
2 . 设
(1)判断函数
的单调性.
(2)是否存在实数a,使得
时,均有
?若存在,求出a的取值范围;若不存在,请说明理由.
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081ad11af2cae38e696f7d4a939434b5.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)是否存在实数a,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b733d17dc0fb4a6720c302960f9037.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa8482499a4211e91159378b69db9a4.png)
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3 . 已知
,
.
(1)对于所有的
,均有
,求实数a的取值范围;
(2)当a=-1时,求函数
在区间
上的最值;
(3)证明:对所有的
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21641326deec4f62f39550bf317221b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76af4731abaa07e3b215e719eeed954.png)
(1)对于所有的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0332c53200cf39826b26fd21e713ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae4b12d8a282854010fdec8e2ec106d.png)
(2)当a=-1时,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f23cc411468a3882011e6a5a5a4e21d.png)
(3)证明:对所有的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc4136bd17997e11a7f8abcb19f9018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43028c46155ecca08c12ba8d9f6be088.png)
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2014高三·黑龙江·竞赛
名校
4 . 已知函数
,
,若关于
的方程
在区间
内有两个实数解,则实数
的取值范围是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc70f21e290bf3427c2147a931461fed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b0eaa4a30c76858d1950ca2cf9f355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351ce9a5502d6c9da885457289ebfb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e21da0e143c842fcafca08050322554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2018-12-05更新
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252次组卷
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4卷引用:2014年全国高中数学联赛黑龙江赛区预赛试题