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Solution:
To find the critical points, solve the equations:
Substituting 
into B,
Therefore, the critical points are (1,1) and (0,0)
Using the Second Derivative Test,
So, (0,0) is a saddle point and f
= -1 is a local minimum.
The graphs below show the geometry of the problem. In the first the function -f(x,y) is graphed on the domain [-0.5, 1.5] x [0.5, 1.5], and shows the min of f(x,y) as a max of -f(x,y). In the second, f(x,y) is graphed on a small domain [-0.25, 0.25] x [0.25, 0.25] to show the saddle at the origin.
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by: sh
