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Jun 01,  · Thanks for contributing an answer to Mathematics Stack Exchange!. Suppose f (a,b) → R^2 is continuously differentiable and the first component (the x component) of ∇ f(t) is not equal to 0 for all t ∈ (a,b) Prove that there exists an interval (c,d) and a continuously differentiable function g (c,d) → R such that (x, y) ∈ f (a,b) if and only if x ∈ (c,d) and y = g(x). R v Y ł B c t e ` i h D b t @ j u c q b c e V O O P O T f B X r v ̓h C c v j \ A _ ̃u hDUFA o E n E X ̑n n ҃ @ ^ ̐ _ ߂ ꂽ X Z R h B.

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