Question

Find the interval for which x=t^2/2-3t+5 and y=t^2+4t-1 is concave up and concave down

Answer 1

you need to check y" for positive or negative
y' = (dy/dt) / (dx/dt) = (2t+4)/(t-3)
y" = dy'/dx = d/dt (2t+4)/(t-3) / (dx/dt) = -10/(t-3)^3
So it looks like it is concave
up for t<3
down for t>3

Answer 2

So, concave up (-∞,3) and concave down (3,∞)???