f(x)=cosx(sinx+cosx)
=sinxcosx+cos^2x
=1/2sin2x +1/2(cos2x+1)
=1/2(sin2x+cos2x)+1/2
=√2/2(sin2x*√2/2+cos2x*√2/2)+1/2
=√2/2sin(2x+π/4)+1/2
所以最小值是当sin(2x+π/4)=-1时f(x)最小值=1/2-√2/2