(1)
f(x)=2sin^2x+cos^2x-sinxcosx
=sin^2x+sin^2x+cos^2x-sinxcosx
=1+sin^2x-sinxcosx
=1+1/2-1/2cos2x-1/2sin2x
=3/2-1/2(sin2x+cos2x)
=3/2-根号2/2sin(2x+π/4)
2x的周期为2π,即x的周期为π
2nπ-π/2≤2x+π/4≤2nπ+π/2时,即nπ-3π/8≤x≤nπ+π/8时,根号2/2sin(2x+π/4)递增,f(x)==3/2-根号2/2sin(2x+π/4)单调减；
2nπ+π/2≤2x+π/4≤2nπ+3π/2时,即nπ+π/8≤x≤nπ+5π/8时,根号2/2sin(2x+π/4)递减,f(x)==3/2-根号2/2sin(2x+π/4)单调增.
（2）求f(x)的最大值,并求此时自变量x的集合
当sin(2x+π/4)=-1时,f(x)有最大值：
f(x)max=3/2-根号2/2*(-1)=(3+根号2)/2
此时,2x+π/4=2nπ+3/2π
即x=nπ+5π/8,（其中n为整数）