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#a6229533-bdb7-41ec-8d9b-8cc52f779783中等解答题极值点偏移导数

6.已知函数f(x)=xlnx12mx2xf(x)=xlnx-\frac{1}{2}mx^{2}-xmRm\in R
(1)若g(x)=f(x)g(x)=f\prime (x)(f(x)(f\prime (x)f(x)f(x)的导函数),求函数g(x)g(x)在区间[1[1e]e]上的最大值;
(2)若函数f(x)f(x)有两个极值点x1x_{1}x2x_{2},求证:x1x2>e2x_{1}x_{2}>e2