1. The problem statement, all variables and given/known data I'm reading this at the moment: "Let f:R^n-->R^n be of class C^1 (that is, assume Df exists and is continuous)" What does it mean?? If it means that for all x in R^n, the linear map Df(x):R^n-->R^n is continuous, then it's a triviality since all linear maps from R^n to R^m are continuous. So I am skeptical that this is what it means! What other option is there? That map that send x in R^n to the point Df(x) in the space of linear map is a continuous map? I highly doubt that! So what does it mean??