求y=cos^2x-cosx+2的单调区间

2025-06-22 16:41:48
推荐回答(1个)
回答1:

y=cos^2x-cosx+2

=(cosx-1/2)^2+7/4

cosx属于[-1,1],
当cosx从1/2 -> 1时,y单调增

cosx从1/2 -> -1时,y单调增
当cosx从-1 -> 1/2时,y单调减
cosx从1 -> 1/2时,y单调减

再根据y是周期函数(周期是2π),可知,
其单调增区间是[5π/3+2kπ, 2π+2kπ], [π/3+2kπ, π+2kπ]
单调减区间是[π+2kπ, 5π/3+2kπ], [2kπ, π/3+2kπ]