已知函数f(x)=2cos^2 x+2sinxcosx-1 化简后f(x)=√2sin(2x+π/4) 求f(x)在[0,π/2]上的最小值和最大值

f(x)=√2sin(2x+π/4) =√2sin2(x+π/8) ,x在（-3π/8,π/8）是增函数,在（π/8,5π/8）时减函数；
f(x)在[0,π/2]上的最大值为x=π/8时,此时f(x)=√2,最小值在x=π/2时,此时f(x)=-1