I am doing my test corrections and I have all of them except one.

Find the critical points if the function: f(x,y) = 1/3x^3 + 1/2y^2 + xy+1

So far I have one crit point of (0,0), and I have the both partial derivative but I am not sure what other points there are. The partials that I got are:

f'(x) = x^2 + y

f'(y) = y + x

Am I right so far? If so could somebody help me out there rest of the way? I am not familuar with the math text thing but I am trying to learnn