已知函数f(x)=根号3sinxcosx+cos^2 x

f(x)=1/2*根号3*2sinxcosx+(1-cos2x)/2=根号3/2sin2x-1/2cos2x+1=sin(2x+π/6)+1
1、T=2π/2=π +kπ
f(x)∈{0,2}
2x+π/6∈{-π/2+2kπ,π/2+2kπ}y单增
x∈{-π/3+kπ,π/6+kπ}y单增
2、
x∈{π/2,π}
2x+π/6∈{π/6+π,π+2π}
sin(2x+π/6)∈{-1/2,1}
f(x)最大值是2,最小值是1/2