The second derivative test should do the trick.

The second derivative test states:

1. If D > 0 and > 0, then f(a,b) is a local min.

2. If D > 0 and < 0, then f(a,b) is a local max.

3. If D < 0, then f(a,b) is a saddle point.

4. If D = 0, then the test is inconclusive.