\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} It is certainly possible for the set
of critical points of a function defined in ${\bf R}^3$ to be a point
(e.g., $x^2+y^2+z^2$) or a line (e.g., $x^2+y^2$) or a plane (e.g.,
$x^2$). Can you create a function $F: {\bf R}^3 \to {\bf R}$ whose set
of critical points is all of the twisted cubic, ${\bf c}(t) =
(t,t^2,t^3)$?









\vfil\eject\end

