设函数f（x）=coswx（根号3wsinwx+coswx）,其中0＜w＜2,

f（x）=coswx（√3wsinwx+coswx）＝√3sinwxcoswx＋cos²wx＝√3/2sin2wx＋(1＋cos2wx)/2
＝√3/2sin2wx＋1/2cos2wx＋1/2＝sin(2wx＋π/6)＋1/2
(1)∵最小正周期为π ∴2π/(2w)＝π ∴w＝1 ∴f(x)＝sin(2x＋π/6)＋1/2
∵-π/6≤x≤π/3 ∴-π/3≤2x≤2π/3 ∴-π/6≤2x＋π/6≤π
∴﹣1/2≤sin(2x＋π/6)≤1 ∴0≤f(x)≤3/2
(2)∵函数f（x）的图像的一条对称轴为x=π/3 ∴sin(2w×π/3＋π/6)＝±1
∴(4w＋1)π/6＝2kπ±π/2 ∴w＝3k－1或3k＋1/2
∵0＜w＜2 ∴w＝1/2

1）f(x)=√3coswxsinwx+(coswx)^2=(√3/2)sin2wx+(1/2)(1+cos2wx)
=sin(2wx+π/6)+1/2
若f（x）的最小正周期为π;则T=2π/2w=π; w=1;
f(x)=sin(2x+π/6)+1/2;
当-π/6≤x≤π/3时; -π/6≤2x+π/6≤5π/6;
-1/2≤sin(2x+π...

0≤f(x)≤3/2
w＝1/2