Hello, My textbook says that to determine concavity we calculate the second derivative of the curve. This is a problem from my book, x = t^2 and y = t^3 - 3t the second derivative of this is (3(t^2+1))/(4t^3) I know all the steps to get to this point.. However, the book says that the curve is concave upward when t > 0 and concave downward when t < 0. Can somebody please explain to me what values this last statement refers to. Is there a general theorem/procedure that I can apply to any second derivative of a parametric curve to determine the concavity? Thanks alot in advance.