Folium of Descartes
Find the local extreme points for local functions defined by implicit function theorem for
From this relation we have
Extreme points are between solutions of and y'(x)=0 ,or
Solution x=0 is of no interest as near point (0,0) implicit function theorem is not applicable.
We have and
For we have so
As second derivative is negative in implicit function has a local maximum point in with value