3. Consider the function f(r, y) = 4x² + 4y² – 4x + 4 defined on R². (i) Compute all critical points of f and classify them as either local maxima, local minima or saddle points. (ii) Compute the global maxima and global minima of f, if they exist. If they do not exist, explain why (i.e., prove it). (iii) Let D = {(r, y) € R² | r² + 4y² < 4} and assume f(r, y) is defined on D. Com- pute the global maxima and global minima and discuss their existence (use both approaches, i.e., the Lagrange Multipliers Principle and the analysis of f(x, y) on the boundary of D, ƏD).

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