Question
The swallowtail catastrophe curves are defined by the parametric equations $x=2 c t-4 t^{3}, y=-c t^{2}+3 t^{4}$.Graph several of these curves. What features do the curves have in common? How do they change when $c$ increases?
Step 1
The equations are $x=2 c t-4 t^{3}$ and $y=-c t^{2}+3 t^{4}$. These equations define a family of curves known as the swallowtail catastrophe curves. The parameter $c$ determines the specific curve within this family. Show more…
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