Implicit function theorem
= Implicit function theorem
{wiki}
If $F(x_0,y_0)=0$ and the partial derivative with respect to $y$ is invertible at $(x_0,y_0)$, then the nearby zero set is the graph $y=g(x)$ of a continuously differentiable function.
= Implicit function theorem
{wiki}
If $F(x_0,y_0)=0$ and the partial derivative with respect to $y$ is invertible at $(x_0,y_0)$, then the nearby zero set is the graph $y=g(x)$ of a continuously differentiable function.