Find the absolute maximum and minimum values of f on the set d.

Find the absolute maximum and minimum values of f on the set D.

f(x, y) = 4x + 6y - x2 - y2 + 2,


D = {(x, y) | 0 <= x <= 4, 0 <= y <= 5}

If possible, could you also help with:
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)

f(x, y, z) = 14x + 18y + 12z;    x2 + y2 + z2 = 166

Answer

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