Vertical tangent

A tangent line parallel to the vertical coordinate axis. For a regular level set $\Phi (x,y)=C$, the conditions $\partial \Phi /\partial y=0$ and $\partial \Phi /\partial x\ne 0$ make the tangent line vertical: the relation $d\Phi =0$ forces $dx=0$. The implicit function theorem then expresses $x$ locally as a differentiable function of $y$, although a graph $y(x)$ has no finite derivative there. The curve $x=y^2$ at the origin is a simple example.