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Given a function [tex] r:\mathbb{R} \rightarrow \mathbb{R}^2, r(t) = (f_1(t), f_2(t))[/tex], is there a way to analytically determine if there are points (x1, x2) where r(t) = (x1, x2) for multiple t-values?

Lets say i was to find such points for the function [tex] r(t) = (t^3-t, 3t^2 + 1) [/tex]

How should i go about finding the points without having to plot the graf?

Thanks!

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# Parameterized function crosses own path

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