名校
1 . 已知函数
.
(Ⅰ)若
,求
的单调区间;
(Ⅱ)是否存在实数
,使得
的最小值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fe7f3e7af7c1899cad2c8db79ac766.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(Ⅱ)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 关于函数
,下列命题中所有正确结论的序号是______ .
①其图象关于
轴对称; ②当
时,
是增函数;当
时,
是减函数;
③
的最小值是
; ④
在区间
上是增函数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc6b6c879214d9cae6a9062339a0b59.png)
①其图象关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be86115324901b427f6a0cf3a4c8a5c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47427934d2d5f1c3de9a8f648a33a811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ff22a861c53d7373715281e371c8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505c98f3e49ff5da391509d22464c114.png)
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名校
3 . 定义在R上的函数
,当
时,
,且对任意的
都有
.
(Ⅰ)求证:
是R上的增函数;
(Ⅱ)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40d5295942e85ec07a3728c7ad308d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402dc8125eed2dac02913f5eaaf7fc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9308bb553e88185db6f98a757f0aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01948906f3b7096a102f2b52d1ccbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb81baf89ef03f986cc1e41aaa5b3ce.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
(Ⅱ)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b53901a96f93dce5b59b117f78eaa4d.png)
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2019-01-08更新
|
748次组卷
|
2卷引用:福建省泉州市南安第一中学2017-2018学年高一上学期期中考试数学试题
解题方法
4 . 设函数
,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
(1)当
时,解关于
的不等式:
;
(2)若
且
,已知函数
有两个零点
和
,若点
,
,其中
是坐标原点,证明:
与
不可能垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d4985bfa06dbd6c3d8faff88b0d192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64afd5ad06ba91a2f620fa81fec3894c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01162b9ae6aa69dd858f7d807c708f4e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e7deb668cee7b52f8b35ae95ed4d0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9eea5fd36d96291ce2e62d24d9f75a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ce91cc8d671a51948e8aae8e12f8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
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