Question

已知w＞0，函数f（x）=sin（wx+π/4）在（π/2，π）上单调递减，则w的取值范围是？

Answer 1

f（x）=sin（wx+π/4）(w>0)的减区间由(2k+1/2)π<wx+π/4<(2k+3/2)π，k∈Z确定，
各减π/4，(2k+1/4)π<wx<(2k+5/4)π，
各除以w,(2k+1/4)π/w<x<(2k+5/4)π/w,
f(x)在（π/2，π)递减，
∴(2k+1/4)π/w<=π/2，π<=(2k+5/4)π/w，
∴(2k+1/4)/w<=1/2，1<=(2k+5/4)/w，
∴(4k+1/2)<=w<=(2k+5/4),
∴k<=3/8,
∴k=0，1/2<=w<=5/4，为所求.