\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose $\displaystyle f(x) =
{{{5x^2-10x}\over {e^x}}}$.

\smallskip

\noindent a) Graph $y = f(x)$ in the window $0 \leq x \leq 5$ and $-3\leq y
\leq 1$. Locate the apparent highest and lowest points on the curve.

\medskip

\noindent b) Calculate $f'(x)$ and use it to locate (algebraically) all those
values of $x$ at which the graph has a horizontal tangent line. Check
your answer against a).

\medskip

\noindent  c) Use $f'(x)$ to find an equation for the line that
is tangent to the curve $y = f(x)$ at $x = 1$. Draw the line on the
graph in a) to check the result.

\medskip

\noindent  d) Use the graph in a) to guess the values of $x$ where $f'(x)$ is
largest and where $f'(x)$ is smallest. Then graph the equation
$y=f'(x)$ on your calculator to check your guesses.


\vfil\eject\end

