1. 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) ?

2. Originally Posted by coe236
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 ?
correct

b) dy/dt=6*x*(dy/dt)
dy/dt=6*x*3=18x ?
we are traveling in the positive direction, since dx/dt is positive. this means as t gets larger, x also gets larger. but dy/dt depends on x, so as x gets very large, so does dy/dt. it will goes to infinity.

c) ?
it would have to get smaller. as t gets large, so does x. since x is getting large, we want dx/dt to keep getting smaller so we can maintain a constant dy/dt

3. that makes sense. Thanks!