derivatives/ implicit differentiation

I tried to work out this problem and I got some answers, but I'm highly doubtful about them. Can someone reassure me please.

**An Object is moving along the parabola y=3x^2 **

**a) when it passes through point (2,12), its horizontal velocity is dx/dt=3. What is its vertical velocity at that instant?**

**b) If it travels in such a way that dx/dt=3 for all t, then what happens to dy/dt as t approaches (+)infinity?**

**c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dx/dt at t approaches (+)infinity?**

My Work:

a) dy/dt=6*x*(dx/dt)

dy/dt=6*2*3=36 ?

b) dy/dt=6*x*(dy/dt)

dy/dt=6*x*3=18x ?

c) ?