解一题:分段函数f(x)={①sinx,cosx≤sinx ②cosx,sinx<cosx},求其增区间?
问题描述:
解一题:分段函数f(x)={①sinx,cosx≤sinx ②cosx,sinx<cosx},求其增区间?
答
1.x∈[2kπ,2kπ+π/4] 单减
2.x∈[2kπ+π/4,2kπ+π/2] 单增
3.x∈[2kπ+π/2,2kπ+5π/4] 单减
4.x∈[2kπ+5π/4,2kπ+2π] 单增
故增区间为 x∈[2kπ+π/4,2kπ+π/2]∪[2kπ+5π/4,2kπ+2π]