∵y=√2/4sin(π/4-x)+√6/4cos(π/4-x)
=√2/2sin(π/4-x+π/3)=-√2/2sin(x-7π/12)
∴最小正周期T=2π
单调增时：2kπ+π/2≤x-7π/12≤2kπ+3π/2 k∈Z
∴单调增区间为 [2kπ+13π/12,2kπ+25π/12] k∈Z