Let f(x)=x^{3}+3 x^{2}+1. There is a unique line of the form y=m x+b such that m>0 and this line intersects f(x) at three points, A, B, C such that A B=B C=2. Find \lfloor 100 m\rfloor.
Let f(x)=x^{3}+3 x^{2}+1. There is a unique line of the form y=m x+b such that m>0 and this line intersects f(x) at three points, A, B, C such that A B=B C=2. Find \lfloor 100 m\rfloor.