How can I find the critical points for this function:

f(x,y)=x^2+y^2+(1/x^2y^2)

graph of x^2/(x^4+1)

graph of x^2/(x^4 + 1)

There is nothing special about this function of two variables. Just use the definition of a critical point. You will have to find partial derivatives and solve a couple of equations.