\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Consider the function
$F(x,y)=x^3+ye^{x-2}$; note that $F(2,1)=9$.

\medskip

 \noindent a) Find the equation of the tangent plane to the graph of
$F$ (the surface $z=F(x,y)$) at the point $(2,1,9)$, and find the
equation of the line in which this plane intersects the $xy$-plane.

\medskip

\noindent b) Find the equation of the tangent to the level curve
$F(x,y)=9$ at the point $(2,1)$.  

\medskip

\noindent c) Show that the lines found in a) and b) are parallel.
Is this an accident? Explain.

\vfil\eject\end

