3 7. Let f: R² → R be given as f(x) = x₁³ - 3 B x₁ x₂ + x₂³ for some ß E R. Determine the nature of critical points of this function for all values of ß, i.e. indicate if a critical point is a (strict) local or global minimizer (maximizer) or a saddle point.

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2. If f(2) = e*, describe the images under f(z) of horizontal and vertical lines, i.e. what are the sets f(a + it) and f(t + ib), where a and b are constants and t runs through all real numbers?