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函数f(x)=∑9n=1|x-n|的最小值为().A·190B·171C·90D·45解法1利用不等式|a|+|b|≥|a+b|∵∑9n=1|x-n|≥|x-1+19-x|+|x-2+18-x|+…+|x-9+11-x|+|x-10|=90+|x-10|≥90,当且仅当x=10时所有的等号成立,∴[f(x)]min=90.选C.解法2借助绝对值的几何意义由绝对值的几何意义知:问题
The minimum value of the function f(x)=∑9n=1|xn| is (). A·190B·171C·90D·45 Solution 1 Use the inequality |a|+|b| ≥|a+b|∵∑9n= 1|xn|≥|x-1+19-x|+|x-2+18-x|+...+|x-9+11-x|+|x-10|=90+|x-10| ≥ 90, if and only if x = 10 all the equal signs hold, ∴ [f (x)] min = 90. Select C. Solve 2 The geometric meaning of the absolute value is known from the geometric meaning of the absolute value: