## Folium of Descartes

Posted November 21st, 2007 by Structure

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