parametric curve with rates

Examine a curve defined parametrically.[br]Left panel shows curve; right panel can show first & second derivatives of y with respect to x.[br][br]Enter coordinate functions for C(t)=(X(t),Y(t)) at top of left panel [use variable t].[br]Enter ends of parameter interval [Lo,Hi] at bottom of left panel.
A slider specifies number T for point C(T) to be marked on the curve;[br]animation shows how that point moves as T increases from Lo to Hi.[br](To change T by 0.01, click-on T and use left- or right-arrow key.)[br][br]A checkbox in left panel gives an option for the velocity vector at C(T) to be displayed.[br]Checkboxes in right panel give options to display slope and concavity info for the curve.

Information: parametric curve with rates