若函数f(x)=xcos(2x-π/4)-1/2sin(2x-π/4)(0

问题描述:

若函数f(x)=xcos(2x-π/4)-1/2sin(2x-π/4)(0

用求导做
f(x)的导数=cos(2x-π/4)-2xsin(2x-π/4)-cos(2x-π/4)=-2xsin(2x-π/4)
令f(x)的导数=0,则x=π/8或5π/8,再列表就能求出单调增区间为(0,π/8)和(5π/8,π)
单调减区间为(π/8,5π/8)