. Let f(x, y) = ² - 2xy + 2y? – x +3. (a) Determine all the critical points of f. (b) Determine the nature of each critical point of f. (c) Determine the maximum and minimum of f on the boundary of the triangle with vertices (0,0), (2,0) and (1,1). (d) Determine the absolute maximum and minimum of f over the entire triangle with vertices (0,0), (2,0) and (1,1).

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