Are you sure (-1, -1) is the maximum of z? For a function that is continuous on a closed interval we know that the function will achieve its extrema at some f(a) and f(b) with a and b contained in the closed interval, and f'(a)=f'(b)=0. How can you get the interval on which z is continuous to be closed?

If you are still struggling, a good first step would be to reconsider your statement that z(-1, -1) does not exist.