某企业每月生产x件产品的总成本为C(x)＝x2＋60x＋400(万元)，求每月产量为多少件时平均成本最低?

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问题某企业每月生产x件产品的总成本为C(x)＝

x²＋60x＋400(万元)，求每月产量为多少件时平均成本最低?

选项

答案根据题意，平均成本为 f(x)=[*]（x＞0) 从而，f’(x)=[*]．令f’(x)=0，得x=200或-200(舍去)．函数f(x)在(0，+∞)内仅有一个驻点x=200，所以每月产量为200件时平均成本最低．

解析

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本试题收录于：数学题库普高专升本分类

数学

普高专升本

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某企业每月生产x件产品的总成本为C(x)＝x2＋60x＋400(万元)，求每月产量为多少件时平均成本最低?

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