parametric equations, points of tangency

[Guest]

I have 2 questions.

1) Find all points (if any) of horizontal and vertical tangency to the curve.

. . .x = 4(cost)^2
. . .y = 2sint

I took the derivatives of both. dx/dt= -8costsint and dy/dt=2cost From here I am lost.

2) Determine the t intervals on which the curve is concave downward or concave upward.

. . .x = 2 + t^2
. . .y = t^2 + t^3

I assume I need to take the 2nd derivative for concavity. I don't understand what to do once I have the 2nd derivative.

HELP!

Thanks

 

[pka]

First, did you draw a graph? Then look at it.
\(\displaystyle \L\frac{{dy}}{{dx}} = \frac{{ - 1}}{{4\sin (t)}}\)

What t would make the slope zero?
What t would make the slope undefined?