Let [tex]\gamma : R -> R[/tex] is smooth function and [tex]U = {(x,y,z) \in R^3 : x \ne 0}[/tex] - open subset.

Function [tex]f : U -> R[/tex] is defined as [tex]f(x,y,z) = z - x\gamma(y/x)[/tex] and this is smooth function.

Proof that for surface[tex]S = f^{-1}(0)[/tex] all tangent planes passing through coordinates origin.

Can anyone give me a hint?