\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} If $A$ is a positive number, the
parametric curve $ { \cases{x = t^3-t\cr y= {\textstyle
A\vphantom{'}\over {\textstyle{1+t^{2\vphantom{'}}}}}\cr}}$ looks
like:

\medskip

\centerline{\epsfbox{w6A1.eps}}

\medskip

%\noindent There's one value of the number $A$ so that the
%``self-intersection'' of the curve is perpendicular and the picture
%looks like:

\noindent For one value of $A$, the ``self-intersection''
of the curve is perpendicular. The picture looks like:

\medskip

\centerline{\epsfbox{w6A2.eps}}

\medskip

\noindent Find that value of $A$.

\vfil\eject\end