题目

You’re sitting on the train home and the person opposite you yawns(打哈欠). Suddenly, you’re yawning with him, though you’re not tired. This phenomenon confused scientists for years until a recent study found that people tend to sympathize with fellow humans. Supporting this claim was the discovery that those children who were unable to form normal emotional ties with others did not experience contagious(有感染力的) yawning, which showed that humans communicate regularly without words. Hugo Critchley, a neuroscientist, has conducted an experiment recently, which will pr已知函数f（x）=x2+ln x-1．（1）求函数f（x）在区间[1，e]（e为自然对数的底）上的最大值和最小值；（2）求证：在区间（1，+∞）上，函数f（x）的图象在函数g（x）=x3的图象的下方；（3）求证：[f′（x）]n-f′（xn）≥2n-2 （n∈N*）．