\begin{homework}\
\label{homework:4}


\exercise %1.
Using the procedure used above in Example 4.1, find the derivative function
for $y=f(x)=\sqrt{169-x^2}$.

\smallskip

\exercise %2.
Using the procedure that we used in Examples 4.2 and 4.3, find the derivative
function for: (a) $y=f(t)=80-4.9t^2$, (b) $y=f(x)=x^2-(1/x)$, (c) $y=f(x)=
ax^2+bx+c$ (where $a$, $b$, and $c$ are constants), (d) $y=f(x)=x^3$.
Please show every step clearly.


\smallskip

\exercise %3.
For each of the following two graphs $y=f(x)$, use graphical differentiation to
sketch the graph of the derivative function.  For $x$ at regular intervals
from one end of the domain to the other, estimate the derivative $f'(x)$
using a ruler, as explained in the text.  Show clearly the points where the
derivative is zero and where the derivative does not exist (or is
infinite).

\smallskip

%-------------------------
\begin{centering}
\begin{psfigure}{\textwidth}{3.0in}{figDE.ps}
\end{psfigure}\\

\bigskip

\begin{psfigure}{\textwidth}{3.0in}{figDF.ps}
\end{psfigure}\\
\end{centering}
%----------------------------


\smallskip
\newpage

\exercise %4.
The 24 graphs below are labeled by letters from (a) to (x).  For each of
the following graphs of $f(x)$, give the letter of the graph that looks
most like it could be the graph of the derivative function $f'(x)$:

\noindent
(1) b, (2) c, (3) e, (4) g, (5) h, (6) j, (7) l, (8) p, (9) r, (10) s, 
(11) t, (12) u, (13) w, (14) x.

\smallskip
%
%-----------------------------
\begin{centering}
\begin{psfigure}{\textwidth}{4.5in}{figDG.ps}
\end{psfigure}\\
\end{centering}
%----------------------------


\end{homework}

