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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.

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# Homework Help: Parametric Curve Concavity

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