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Local maximum and minimum and saddle points

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Find the local maximum and minimum values and the saddle points of the functions.

1.)f(x,y)= xy(1-x-y)

2.)f(x,y)= (x^2y^2 - 8x + y)/(xy)

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This provides two examples of finding local maximum and minimum and saddle points.

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Find the local maximum and minimum values and the saddle points of the functions.
We need 2nd order derivative test.
Hessian = , and D=
If D is negative, we have a saddle point.
If D is positive, then if > 0, we have a local minimum. If <0, then we have local maximum.

Every other ...

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