题目 编号:94

如果直线http://static.haoxue.com/tk/import/20150823152114/image234.pnghttp://static.haoxue.com/tk/import/20150823152114/image235.pnghttp://static.haoxue.com/tk/import/20150823152114/image236.pnghttp://static.haoxue.com/tk/import/20150823152114/image237.pnghttp://static.haoxue.com/tk/import/20150823152114/image005.png轴正半轴, http://static.haoxue.com/tk/import/20150823152114/image004.png轴正半轴围成的四边形封闭区域(含边界)中的点,使函数http://static.haoxue.com/tk/import/20150823152114/image238.pnghttp://static.haoxue.com/tk/import/20150823152114/image040.pnghttp://static.haoxue.com/tk/import/20150823152114/image124.png)的最大值为8,则http://static.haoxue.com/tk/import/20150823152114/image125.png的最小值(  )",

A.4

B.3

C.2

D.0

答案及解析

答案

A

解析

http://static.vko.cn/content/tk/import/20150823152114/image009.png为封闭区域中的任意点则http://static.vko.cn/content/tk/import/20150823152114/image009.png满足约束条件可行域如图所示,目标函数的最优解为http://static.vko.cn/content/tk/import/20150823152114/image239.png,依题意将http://static.vko.cn/content/tk/import/20150823152114/image239.png代入http://static.vko.cn/content/tk/import/20150823152114/image238.pnghttp://static.vko.cn/content/tk/import/20150823152114/image040.pnghttp://static.vko.cn/content/tk/import/20150823152114/image124.png)得最大值8,解得http://static.vko.cn/content/tk/import/20150823152114/image240.png有基本不等式得: http://static.vko.cn/content/tk/import/20150823152114/image241.png(当且仅当http://static.vko.cn/content/tk/import/20150823152114/image242.png时,等号成立),故http://static.vko.cn/content/tk/import/20150823152114/image125.png的最小值为4 ,故选: A.http://static.vko.cn/content/tk/import/20150823152114/image243.png

举一反三

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