答案:
①∵当x∈[0,2]时,f(x)=(-1)(-4),
∴令2x=t,得f(x)=(t-1)(t-4)=g(t)
当且仅当t=时,[f(x)]min=g()=-,此时x=log2∈[0.2].
②当x∈[-2,0]时,f(x)=f(x+2)=(-1)(-4),
类似①的方法,可得当x=log2∈[-2,0)时,[f(x)]min=-;
③当x∈[-4,-2]时,f(x)=f(x+2)=(-1)(-4)
类似①的方法,可得当x=log2∈[-4,-2)时,[f(x)]min=-;
④当x∈[-6,-4]时,f(x)=f(x+2)=(-1)(-4)
类似①的方法,可得当x=log2∈[-4,-2)时,[f(x)]min=-
综上所述,若f(x)在[2n,2n+2]上的最小值为-时,n=3
故选:D