Given the following function,

ƒ(x, y) = -8x + x2 + 12y + 4y2 – 2xy

Use a package or software library to determine the minimum:

(a) Graphically.

(b) Numerically.

(c) Substitute the result of (b) back into the function to determine the minimum ƒ(x, y).

(d) Determine the Hessian and its determinant, and substitute the result of part (b) back into the latter to verify that a minimum has been detected.

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