Word Count : 390

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To determine if the function \( f(x, y) = x^3 + y + x^2 + y^2 \) is locally invertible at \( (1, 2) \), we can apply the Inversion Theorem, which states that a function is locally invertible at a point if the Jacobian determinant at that point is non-zero. ### Step 1: Find the partial derivatives of \( f(x, y) \). We need __________ ____ _____ _______ __________ _____ _______ _________ _________ ___ __________.
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