Given the following unconstrained problem: f(x,y) = -x^2 + 2xy + y^2 + x - y +...

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Given

the following unconstrained problem:

f(x,y) = -x^2 + 2xy + y^2 + x - y + 9

The point (1/2, 0) satisfies the first and second order conditions to be the global maximum.

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The point (1/2, 0) satisfies the first order conditions, the Hessian is negative definite, so it a local maximum.

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The point (1/2, 0) satisfies the first and second order conditions to be the global minimum.

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The point (1/2, 0) satisfies the first order conditions, the Hessian is indefinite, so it is a stationary point.

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