The curve defined by is known as the folium of Descartes.
MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
The curve defined by x3+y3−9xy=0 is known as the folium of Descartes.
(a) Compute dxdy for the curve in terms of x and y.
(b) Determine all ordered pairs (x,y) on the curve for which the tangent line is horizontal.
(c) For each point found in part (b), verify that the tangent line is not vertical by checking the denominator of dxdy. Provide justification.
(d) Write the equation of every horizontal tangent line to the curve.