Kumagai proved a version of it that holds even for level surfaces of non- differentiable functions, and economists use this result to obtain well- behaved indifference curves from utility relations. It holds for F wherever the Frechet derivative DF is non-singular, that is, where the function's Jacobian is zero, and is equivalent to the inverse mapping theorem in these loc
Kumagai proved a version of it that holds even for level surfaces of non- differentiable functions, and economists use this result to obtain well- behaved indifference curves from utility relations. It holds for F wherever the Frechet derivative DF is non-singular, that is, where the function's Jacobian is zero, and is equivalent to the inverse mapping theorem in these locations.  For ten points, name this theorem which tells us, under certain conditions, that the surface F(x,y) = 0 can locally be solved for y as a differentiable function of x.
Kumagai proved a version of it that holds even for level surfaces of non- differentiable functions, and economists use this result to obtain well- behaved indifference curves from utility relations.
{implicit function theorem}