Question

4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a. (Hint: if ti is the time giving the point (a, b), then consider the timet) (b) (3 points) Sketch the curve. (c) (5 points) Find all the points on the curve where the tangent lines are horizontal or vertical. (For the horizontal tangents, justify using calculus. For the vertical tangents, you can use the symmetry from part (a).)

Answer 1

Please find below the complete answer.

3 It t 27 tf 27 t 6 t f The χ스 - It t, 3 2 tt If t,

TL ズ 一32 70 3 A 2

aan 니 2 73