已知函数F(x)==sinωx+cosωx(ω>0)在(п/2,п)上单调递减,则ω的取值范围是

题目

已知函数F(x)==sinωx+cosωx(ω>0)在(п/2,п)上单调递减,则ω的取值范围是
A.[1/2,5/4] B.[1/2,3/4] C.（0,1/2] D.（0,2]

答案

f(x)=√2sin(ωx+π/4)2kπ+π/2≤ωx+π/4≤2kπ+3π/22kπ+π/4≤ωx≤2kπ+5π/4令k=0,π/4≤ωx≤5π/4π/(4ω)≤x≤5π/(4ω)所以(π/2,π)是[π/(4ω),5π/(4ω)]的子区间π/(4ω)≤π/2且5π/(4ω)≥π解得1/...