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?