f(x)=2sinx(sinx+cosx)=2sin²x+2sinxcosx=1-cos2x+sin2x=sin2x-cos2x+1=√2sin(2x-π/4)+1当2x-π/4=2kπ+π/2,k∈Z即 x=kπ+3π/8,k∈Z时,f(x)取得最大值√2+1五点法画图列表：x π/8 3π/8 5π/8 7π/8 9π/8...