Folium of Descartes

In the applet below, don't click the checkbox yet! Please answer the following question first before proceeding to do so.


The Folium of Descartes has equation . Use implicit differentiation to find at the point (3, 3). Then, use the applet to check your result. (Feel free to move the gray point along the curve wherever you'd like.)


Algebraically determine the coordinates of the point (x, y) on the curve in Quadrant 1 where the tangent line is horizontal.