Let f : R x R → R be differentiable. For each x € R

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Let f : R x R → R be differentiable. For each x € R defined gx: R → R By gx (y) = f(x,y). Suppose that for each x there is a unique y with gx1(y) =0; let c(x) be this y.

Let f : R x R → R be differentiable. For each x € R

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