题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045727-48824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045727-83461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-88630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045727-48824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045727-83461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-10323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-15114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-68395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-68395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-54061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-62756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-30663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-96709.png)
(Ⅰ)求矩形区域
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-88630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-50775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-30663.png)
(Ⅱ)求排管的最小费用及相应的角
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-30663.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-34195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-65925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-30663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-75420.png)
解析
试题分析:(Ⅰ)把
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045730-12862.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045728-68395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045730-61453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-30663.png)
试题解析:(Ⅰ)如图,过
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045730-16570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045730-86177.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045730-41532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045730-68498.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-83998.png)
故有
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-52347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-44679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-50857.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-43533.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-40092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-63117.png)
(Ⅱ)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045731-47425.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-50671.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-32479.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-13815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-89495.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-15940.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-92445.png)
列表
![]() | ![]() | ![]() | ![]() |
![]() | + | 0 | - |
![]() | 单调递增 | 极大值 | 单调递减 |
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-92445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045733-73811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045733-81505.png)
答:排管的最小费用为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045729-65925.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045732-92445.png)
核心考点
试题【如图,某自来水公司要在公路两侧排水管,公路为东西方向,在路北侧沿直线排,在路南侧沿直线排,现要在矩形区域内沿直线将与接通.已知,,公路两侧排管费用为每米1万元,】;主要考察你对常见函数的导数等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045710-49284.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045710-69218.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045710-71706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045710-71122.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045711-41300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045711-94135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045711-81465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045710-69218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045703-93589.png)
(Ⅰ)若f(x)在[2,+∞)上是增函数,求实数a的取值范围;
(Ⅱ)当a=2时,求证:1-
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045703-48422.png)
(Ⅲ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045703-50405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045703-94423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045704-59664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045704-61142.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045704-12819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045655-67654.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045655-96538.png)
(Ⅰ)当f(x)存在最小值时,求其最小值φ(a)的解析式;
(Ⅱ)对(Ⅰ)中的φ(a),
(ⅰ)当a∈(0,+∞)时,证明:φ(a)≤1;
(ⅱ)当a>0,b>0时,证明:φ′(
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045655-73172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045655-58583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045656-18403.png)
A.[-,3] | B.[,6] | C.[3,12] | D.[-,12] |
(1)求常数a的值;(2)若存在x使不等式
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045639-57161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018045639-94830.png)
(3)对于函数y=f(x)和y=g(x)公共定义域内的任意实数x0,我们把|f(x0)-g(x0)|的值称为两函数在x0处的偏差.求证:函数y=f(x)和y=g(x)在其公共定义域内的所有偏差都大于2.
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