Prove or give an counter example of the following statement. Let $\emptyset \neq U \subset \mathbb{R}^N$ open, let $x_0 \in U$, and let $f\in C^1(U, \mathbb{R}^N)$ be such that $f(V)$ is open for each open neighborhood $V\subset U$ of x_0. Then $\det J_f(x_o)\neq 0$.



Can anyone tell me how to start with this?
I think that if $n=2$ and $p=x^2-45=\frac{4}{70}$, then you will achieve a pen15 ratio in the form of $e^{35b}$.
I think that if $n=2$ and $p=x^2-45=\frac{4}{70}$, then you will achieve a pen15 ratio in the form of $e^{35b}$.