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Find the maximum and the minimum of f (x, y) = x^2 + 2xy^2 on the closed disc of radius 1 centered at the origin.

Find the maximum and the minimum of f (x, y) = x^2 + 2xy^2 on the closed disc of radius 1 centered at the origin. Explain how we know that there must be a maximum for this function on this region.

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