Originally Posted by

**Jhevon** critical points in multivariable function are either maximums, minimums or saddle points.

here is the method:

given f(x,y),

find fx, fy, fxx, fyy,fxy

to find the critical points, set fx = 0, and fy = 0

doing this you will obtain one or more points, say (x0, y0), (x1,y1),...

then set up the discriminant equation:

D(x0,y0) = fxx (x0,y0) * fyy(x0,y0) - (fxy(x0,y0))^2

if D>0, and fxx(x0,y0)> 0 we have a local min

if D>0, and fxx(x0,y0)< 0 we have a local max

if D< 0 we have a saddle point