Problem

设\(n\)次函数\(f(x)=x^n+a_1x^{n-1}+\cdots+a_n\)。任意给定\(n+1\)个整数\(x_0,x_1,\cdots,x_n\)，且\(x_0<x_1<\cdots<x_n\)，证明：存在\(x_i\)使得$$|f(x_i)|>\dfrac{n!}{2^n}$$