Exercises 40–49 concern the implicit function theorems and the inverse function theorem (Theorems 6.5, 6.6, and 6.7).
Let S be described by z2 y3 + x2 y = 2.
(a) Use the implicit function theorem to determine near which points S can be described locally as the graph of a C1 function z = f (x, y).
(b) Near which points can S be described (locally) as the graph of a function x = g(y, z)?
(c) Near which points can S be described (locally) as the graph of a function y = h(x, z)?
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