\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Determine the locations of all extreme points of the function
 
$$f(x,y)={1\over1+x^2+y^2},$$
 
\noindent and find the type of each (local min or local max).  Explain
in words what a graph of this function would look like and how that
supports your conclusion.

\medskip

\noindent b) Determine the {\it approximate} location and type of {\it
one} extreme point of the function 
 
$$g(x,y)={1,\!000,\!000\over 1+x^2+y^2}+2x\cos(e^x)+(y+2)(x^4+3xy+17)
 + \ln(1+x^2y^2),$$
 
\noindent possibly by thinking about what the graph of $g$ might look
like. Explain your reasoning carefully.

\vfil\eject\end