[b]In the applet below, [color=#cc0000]d[/color][/b][b][color=#cc0000]on't click the checkbox yet![br][br][/color][/b]Please answer the following question first before proceeding to do so.
1.
The Folium of Descartes has equation [math]x^3+y^3=6xy[/math]. [br]Use implicit differentiation to find [math]\frac{dy}{dx}[/math] at the point (3, 3). [br][br]Then, use the applet to check your result. [br](Feel free to move the [b][color=#444444]gray point[/color][/b] along the curve wherever you'd like.)
2.
Algebraically determine the coordinates of the point (x, y) on the curve in Quadrant 1 where the tangent line is horizontal.
[math]\left(2^{\frac{4}{3}},2^{\frac{5}{3}}\right)[/math], which is approximately equal to (2.5198, 3.1748)