Say we have that f(1)=3, f '(1)=3, g(1)=2, g '(1)=2 and also f(3)=6, f '(3)=1, g(3)=1, g '(3)=0

I found that (f/g)'(1)=0.

What can you assert about (f/g)'(3)?
Is there enough information to calculate f ''(3)?