For each of the following functions f R2 rightarrow R determ

For each of the following functions f: R^2 rightarrow R. determine, with proof, whether the conditions of the local submersion theorem hold at all some, or none of the points of the zero set of f, which is Z(f) = {(x, y) R^2: f(x, y) = 0}. These conditions are: f is continuously differentiable and with non-zero gradient at the point in question. f(x, y)=xy + x f(x, y) = xy+ 1 f(x, y) = (xy)^2 + 1 f(x, y) = (xy + l)^2

Solution

answer (b)