Exercises 40–49 concern the implicit function theorems and the inverse function theorem (Theorems 6.5, 6.6, and 6.7).
Let F(x,y) = c define a curve C in R2. Suppose (x0,y0) is a point of C such that ∇F(x0,y0) ≠ 0. Show that the curve can be represented near (x0,y0) as either the graph of a function y = f (x) or the graph of a function x = g(y).
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