SOLUTION: Find the max/min point for the following function: f (x,y) = x^3 + y^3 + 6xy

Question 1035337: Find the max/min point for the following function:
f (x,y) = x^3 + y^3 + 6xy
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
and .
Also, and , and
Use the Second partial derivative test.
Set the partial derivatives above to 0 and solve for x and y.
and .
This system of equations yield two points as its solutions: (0,0) , (-2,-2). (Verify!!)
Now find the determinant of the hessian for each point.
For (0,0): .
This implies that the point (0,0) is a saddle point (neither a local max nor a local min).
For (-2,-2): .
Since , it follows that (-2,-2) is a local maximum.

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