# Folium of Descartes

Submitted by Structure on Wed, 11/21/2007 - 22:25.

Find the local extreme points for local functions defined by implicit function theorem for

We have

From this relation we have

Extreme points are between solutions of and y'(x)=0 ,or

so

Solution x=0 is of no interest as near point (0,0) implicit function theorem is not applicable.

We have and

Now

For we have so

As second derivative is negative in implicit function has a local maximum point in with value