(1)
因为b>0
当cos(2x+π/6)=-1时有最大值
a+b=3/2 1
当cos(2x+π/6)=1时有最小值
a-b=-1/2 2
1式+2式得
a=1/2
1式-2式得
b=1
(2)
g(x)=-4*(1/2)sin(1x-π/3)
=-2sin(x-π/3)
当sin(x-π/3)=1时有最小值-2
即x-π/3=2kπ+π/2
x=2kπ+5π/6