Answer:
 A(-1,0) is a local maximum point.
B(-1,0)  is a saddle point
C(3,0)  is a saddle point
D(3,2) is a local minimum point.
Step-by-step explanation:
The given function is  

The first partial derivative with respect to x is  

The first partial derivative with respect to y is  

We now set each equation to zero to obtain the system of equations;


Solving the two equations simultaneously, gives;
 and
  and 
The critical points are 
A(-1,0), B(-1,2),C(3,0),and D(3,2).
Now, we need to calculate the discriminant, 

 But, we would have to calculate the second partial derivatives first.





At A(-1,0),
 and
 and 
 Hence A(-1,0) is a local maximum point.
See graph
At B(-1,2);
 
 
Hence, B(-1,0) is neither a local maximum or a local minimum point.
This is a saddle point.
At C(3,0)
 
 
Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.
At D(3,2),
 and
 and 
Hence D(3,2) is a local minimum point.
See graph in attachment.