1. Consider the set S: S = {(x, y, z, w) ≤ R¹ : x² + y² + z² +w² = 1,x+y=1} (a) Show that any point in S can be written locally as the graph of a C¹ function. (b) Which point on the surface S is the farthest away from the point (0, 0, 2, 0)?

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