令3x-π/6=kπ,得对称轴方程是x=kπ/3-π/18
x∈[0,π/3] (3x-π/6)∈[-π/6,5π/6] cos(3x-π/6)x∈[-√3/2,1]
2cos(3x-π/6)x∈[-√3,2]
所以,f(x)最大值是2,最小值是-√3