f(x)=√2*cosx*sin(x+π/4)-1/2
=√2*cosx*(√2/2*sinx+√2/2*cosx)-1/2
=sinxcosx+(cosx)^2-1/2
=1/2*sin2x+1/2*(1+cos2x)-1/2
=1/2*sin2x+1/2*cos2x
=√2/2*(√2/2*sin2x+√2/2*cos2x)
=√2/2*sin(2x+π/4)
令2x+π/4=kπ+π/2,所以x=kπ/2+π/8,所以对称轴为x=kπ/2+π/8 (k∈Z)
f(x)的最小值f(x)min=-√2/2