On what intervals of t is the curve described by the given parametric equation concave up? Concave down?
x=t^2; y=t^(3)+3t
y' = dy/dx = 3t^2 / 2t = 3t/2
dy'/dt = 3/2
y" = dy'/dt ÷ dx/dt = 3/2 ÷ 2t = 3/(4t)
Now it should be smooth sailing
x=t^2; y=t^(3)+3t
dy'/dt = 3/2
y" = dy'/dt ÷ dx/dt = 3/2 ÷ 2t = 3/(4t)
Now it should be smooth sailing