f(x)=(1+cos2x)/4+(1/2)sin2x+3(1-cos2x)/4
=(1/2)sin2x-(1/2)cos2x+1
=(√2/2)sin(2x-π/4)+1
(1)最小正周期为T=2π/2=π
(2) 最大值是√2/2+1,最小值是-√2/2+1
(3) 增区间
2kπ-π/2≤2x-π/4≤2kπ+π/2,k∈Z
2kπ-π/4≤2x≤2kπ+3π/4,k∈Z
kπ-π/8≤x≤kπ+3π/8,k∈Z
增区间是[kπ-π/8,kπ+3π/8],k∈Z
减区间
2kπ+π/2≤2x-π/4≤2kπ+3π/2,k∈Z
2kπ+3π/4≤2x≤2kπ+7π/4,k∈Z
kπ+3π/8≤x≤kπ+7π/8,k∈Z
减区间是[kπ+3π/8,kπ+7π/8],k∈Z