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1数学模型f(x)=∑ni=1mi|x-ai|最值问题的讨论对于一元线性绝对值函数f(x)=∑ni=1mi|x-ai|,其中mi0,i=1,2,…,n,a1a2…an的最值问题可以通过以下定理得出结论.定理1若f(x)=m1|x-a1|+m2|x-a2|,m10,m20,a1a2,则1·当m1m2时,函数f(x)在x=a1处取得最小值f(a1);2·当m1m2时
1 Mathematical model f(x) = ∑ni = 1mi | x - ai | Discussion of the most-valued problem For a one-member linear absolute value function f(x) = ∑ni = 1mi|x-ai|, where mi0,i = 1, The maximum value problem of 2,...,n,a1a2...an can be concluded by the following theorem. Theorem 1 If f(x)=m1|x-a1|+m2|x-a2|,m10,m20,a1a2, then 1. When m1m2, the function f(x) obtains the minimum value f(a1) at x=a1; 2. When m1m2