已知函数f(x)=2sin(2x+π/6) 当X∈[-π,π]时,求f(x)的单调递减区间

题目

已知函数f(x)=2sin(2x+π/6) 当X∈[-π,π]时,求f(x)的单调递减区间

答案

令　2kπ+π/2≤2x+π/6≤2kπ+3π/2
则　kπ+π/6≤x≤kπ+2π/3
令k=-1,0,得
　f(x)在∈[-π,π]上的减区间为[-5π/6,-π/3]和[π/6,2π/3].