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\begin{document}
\centerline{MATH 133 -- Calculus with Fundamentals 1}
\centerline{Quiz 5 -- October 29, 2015}
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\noindent
Your Name: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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\noindent
{\it Directions}
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Do all work in the space provided below or on the back of the second sheet.  There are 30 total points possible.  You may use a calculator.  
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\noindent
{\it Questions}
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\begin{enumerate}
\item[1)] 
\begin{enumerate}
\item[(a)] (5) Find the derivative using the ``short-cut'' rules
(i.e. you {\it do not} need to compute the limit of the difference quotient): 
$f(x) = 8 x^{5/4} + 3x^4 + e^x$
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\item[(b)] (5) Use the limit of the difference quotient to compute $g'(x)$ for 
$g(x) = 5x^2 + x$.
\end{enumerate}
\vfill\eject
\item[2)] The graph above is $y = f(x)$.  
\begin{figure}
\begin{center}
\includegraphics[width=.5\linewidth]{fplot.png}
\end{center}
\end{figure}
\begin{enumerate}
\item[(a)] (4) Over which interval(s) is $f'(x) > 0$?  $\underline{\qquad\qquad\qquad\qquad\qquad}$.
\item[(b)] (4) Over which interval(s) is $f'(x) < 0$?  $\underline{\qquad\qquad\qquad\qquad\qquad}$.
\item[(c)] (2) For which $x$ is $f'(x) = 0$?  $\underline{\qquad\qquad\qquad\qquad\qquad}$.
\end{enumerate}
\vfill\eject
\item[3)] The graph above is $y = g(x)$.  
\begin{figure}
\begin{center}
\includegraphics[width=.5\linewidth]{Discont.png}
\end{center}
\end{figure}
\begin{enumerate}
\item[(a)] (5) Is $g$ differentiable at $x = 2$?  Why or why not?  
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\item[(b)] (5) Does $g$ appear to be differentiable at $x = 1.5$?   Why or why not?  
\end{enumerate}
\end{enumerate}
\end{document}
