These are the critical points.
I hope you've done bits of algebra including matrices...
The Hessian matrix is defined at a point as :
Work with eigenvalues
If the eigenvalues are all positive, then this point is a maximum.
If they are all negative, then this point is a minimum.
If one is positive and one is negative, then this point is a saddle point.
Work with discriminant
If the discriminant is negative, then it's a saddle point.
If the discriminant is positive and , then it's a maximum.
If the discriminant is positive and , then it's a minimum.
If you don't know how to proceed, google for Hessian matrix.