.
Solution:
To find the critical points, solve the equations:
Substituting B into A,
At 
the function f(x, y) is undefined, therefore only one critical point exists:
(-1/2,4)
Using the Second Derivative Test,
So, f(-1/2,4) = -6 is a local maximum.
The plot below is graphed on a circle of radius 1/10 centered at (-1/2,4). It confirms the fact that there is a local maximum at (-1/2,4).
by:sh