y=|2sin2x|的单调区间怎么求

Question

如题所述

Answer 1

y = |2sin(2x)|
sinx的周期为2π, sin(2x)x的周期为π, |2sin(2x)|将2sin(2x)的图像在x轴下方的部份翻折到x轴上方，周期为π/2
现在考虑(0, π/2)内的情况:
x = π/4: y = |2sin(2x)| = 2, 此为y的最大值
x = 0, x = π/2: y = 0
增区间: (kπ/2, π/4 + kπ/2)
减区间:(π/4 + kπ/2, π/2 + kπ/2)
k为整数