y=sinx+cosx+2sinxcosx+2cosx =1+sin2x+cos2x+1 =2+sin2x+cos2x =2+√2sin(2x+π/4) 当2x+π/4=2kπ+π/2时,有最大值2+√2,x=kπ+π/8,k∈z 当2x+π/4=2kπ-π/2时,有最小值2-√2,x=kπ-3π/8,k∈z