8. Let                        f(x, y) = x + sin(x + 2y).Find the unit vector in the direction in which f increases most rapidly at the point (0, 0) and give the rate of change of f in that direction.

(3) To create an open box from a square piece of cardboard, we can cut out identical squares from each corner and then fold up the resulting flaps. If the cardboard measures 10 inches on each side, determine the dimensions of the box that will yield the maximum volume. Note: Points will be awarded only if calculus is used in the solution.

8. Let
f(x, y) = x + sin(x + 2y).
Find the unit vector in the direction in which f increases most rapidly at the point (0, 0) and give the rate of change of f in that direction.

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