已知,函数f(x)＝2sinx(sin x＋cos x) 求,〔1〕f(x)的最小正周期,和最大值

f(x)=2sinx(sin x＋cos x)
=2(sinx)^2+2sinx*cosx
=-[1-2(sinx)^2]+2sinx*cosx+1
=sin2x-cis2x+1
=√2*(√2/2*sin2x-√2/2*cos2x)+1
=√2*(sin2x*cosπ/4-cos2x*sinπ/4)+1
=√2*sin(2x-π/4)+1.
f(x)的最小正周期为：T=2π/2=π,
最大值为：√2+1.