stationary points for functions of two variables

hi, i have a question concerning stationary points of functions of two variables, i have a problem sheet question - i have done the problem and got the answer but my class mate disagrees with my answer, im trying to find out who is right, its annoying me,

the problem is:

__Find and classify the stationary points of the following function:__

f(x,y) = 1/3x^3 + 1/3y^3 - x^2 - y^2

I have worked out that there are four stationary points at the following coordinates:

(0,0) Maximum

(0,2) Saddle point

(2,0) Saddle point

(2,2) Minimum

My friend thinks there are only two stationary points -the maximum and minimum points from above,

Could anybody help with this problem and settle the score for us as i hate admitting im wrong (Lipssealed)(Rofl)

Any help is appreciated

Thank you

missmath