posted by John .
An object is moving along the parabola y = 3x^2. (a) When it passes through the 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 --> +infinity? (c) If, however, it travels in such a way that dy/dt remains constant, then what happens to dy/dt as t --> +infinity?
dy/dt = 6x(dx/dt)
so at (2,12) dx/dt = 3
then dy/dt = 6(2)(3) = 36
If dx/dt is always 3, then dy/dt = 18x
so as x --> + infinity , 18x ---> + inf.
and dy/dt --> + inf.
for c) I think you meant to say,
"then what happens to dx/dt as t --> +infinity?"
if dy/dt = c
then c = 18(dx/dt)
dx/dt = c/(18x), now as x becomes larger and larger, what happens to the c/(18x) , and as a result, what happens to dx/dt ?
its not right