探究函数
,x∈(0,+∞)取最小值时x的值,列表如下:
请观察表中y值随x值变化的特点,完成以下的问题:
(1)函数
(x>0)在区间(0,2)上递减;函数
在区间________上递增.当x=_________时,
_______.
(2)证明:函数
(x>0)在区间(O,2)上递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
x | … | 0.5 | 1 | 1.5 | 1.7 | 1.9 | 2 | 2.1 | 2.2 | 2.3 | 3 | 4 | 5 | 7 | … |
y | … | 8.5 | 5 | 4.17 | 4.05 | 4.005 | 4 | 4.005 | 4.02 | 4.04 | 4.3 | 5 | 5.8 | 7.57 | … |
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22ffecf6270810f2533abbcf5edf6b0.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4426903eb63c0cf1b8e19d97f25398f.png)
更新时间:2019-11-05 15:48:49
|
相似题推荐
解答题-问答题
|
适中
(0.65)
名校
【推荐1】已知函数
的定义域为
.
(1)若非空集合
满足
,求实数a的取值范围;
(2)若
,用定义证明:
是定义域上的严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81a414323589af4ed230c17aa2faf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26322bd1e71fa74bb84a3ac150414a2.png)
(1)若非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f061ce46cb17bd8339322b4ed04219b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9afa6ca3c54f758947c5ece1a2e71b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69f28de04e6340b47f82e84446b83a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐2】设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103443e36075a1eeacdabb8ab6f2e833.png)
(1)求函数
的图像与直线
交点的坐标:
(2)当
时,求函数
的最小值
(3)用单调性定义证明:函数
在
上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103443e36075a1eeacdabb8ab6f2e833.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966b60302d80d8613675bb3dd5c03164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)用单调性定义证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4a226feca9d9095b0f68191245ed22.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
解题方法
【推荐3】已知定义在R上的奇函数
=
.
(1)求实数
的值;
(2)判断
的单调性,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e8f9f4e879a16cddb092243274687ee.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0877194ab8760f54c35527177b03ff93.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
名校
【推荐1】已知函数
是定义在
上的偶函数,当
时,
.现已画出函数
在
轴右侧的图象,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/f34f2c2a-375b-4c78-8e44-5e6590611b12.png?resizew=315)
(1)画出函数
在
轴左侧的图象,根据图象写出函数
在
上的单调区间;
(2)直接写出
在
上的解析式,并求
在区间
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5749bb82edfb623c63ae4ec6b4d43da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/f34f2c2a-375b-4c78-8e44-5e6590611b12.png?resizew=315)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7996d044a6d5332b9b9675f638715.png)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
【推荐2】已知
,
,
.
(1)求函数
的定义域并画出
的图像
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d67bf895-cc91-47bb-9ea3-f5cf6429b66c.png?resizew=174)
(2)写出函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cc7b74563f9b086bae22bf33e43c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c3fa9706da43cdf1a42c646374709a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a2b2e30ac8ef8c9c940b5ad69a6a4d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1776097ac2b4b38d83b20656ffc762e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5790d5181783c15fd46d95bf18b796f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/d67bf895-cc91-47bb-9ea3-f5cf6429b66c.png?resizew=174)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1776097ac2b4b38d83b20656ffc762e0.png)
您最近一年使用:0次