\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $C$ is a {\it positive}\/
real number, and $f(x)=C-x^4$.

\medskip


\noindent a) Sketch the region {\bf R} bounded by $y=f(x)$ and the
$x$- and $y$-axes \underbar{in the first quadrant}. \underbar{Label
the region {\bf R}.}

\medskip

\noindent b) Compute the area of {\bf R}. Your answer will use the
parameter $C$.

\medskip

\noindent c) Suppose {\bf R} is revolved around the
\underbar{$y$-axis}. Find the volume of this solid object.  Your
answer will use the parameter $C$.

\medskip

\noindent d) For which value of $C$ will the volume found in c) be
equal to 1?


\vfil\eject\end