Problem

Source: 2021ChinaTST test4 day2 P1

Tags: Inequality, algebra, TST



Suppose $x_1,x_2,...,x_{60}\in [-1,1]$ , find the maximum of $$ \sum_{i=1}^{60}x_i^2(x_{i+1}-x_{i-1}),$$where $x_{i+60}=x_i$.