(1)由题意知: 1+b= 3 a 1×b= 2 a a>0 ,解得a=1,b=2.(2)由(1)知a=1,b=2,∴A={x|1<x<2},f(x)=4x+ 9 x (1<x<2),而x>0时,4x+ 9 x ≥2 4x? 9 x =2×6=12,当且仅当4x= 9 x ,即x= 3 2 时取等号,而x= 3 2 ∈A,∴f(x)的最小值为12.