This is an elliptic paraboloid, having a single minimum.
The two partial derivatives are zero only at (0, 0).
This is the only critical point.
Now, we could the second partials test.
Since D > 0, we examine f-xx. Since f-xx = 4 > 0, this is a (local) minimum.
However, we might also skip the partials test. We observe that since both variables are squared, the global minimum value must occur where x = 0 and y = 0. That is, the minimum value is