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\centerline{MATH 133 -- Calculus with Fundamentals 1}
\centerline{Quiz 8 -- December 1, 2017}
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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.   
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\noindent
{\it Questions}
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\begin{enumerate}
\item[1)]  Both parts of this question refer to the function $f(x) = x^2 e^{-4x}$
\begin{enumerate} 
\item[(a)] (5) Compute $f'(x)$.
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\item[(b)] (5) Find the critical points of $f$ from your derivative.   
\end{enumerate}
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\item[2)]  The graph above shows $y = f'(x)$ for some function $f$  (NOTE:  this is the 
graph of the derivative $y = f'(x)$, NOT $y = f(x)$).
\begin{figure}
\begin{center}
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\caption{Plot of $y = f'(x)$ for Problem 2}
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\begin{enumerate}
\item[(a)] (4) What are the critical points of $f$ in the interval $[-4,4]$? 
\item[] Answer: $x = \underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\item[(b)] (4)  At which $x$ value(s) in this interval does $f$ have a local maximum?
\item[] Answer: $x = \underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\item[(c)] (4) Explain briefly how you know your answer in (b) is correct.
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\item[(d)] (4)  On the interval $(-1,1)$, is the graph $y = f(x)$
concave up or concave down? 
\item[] Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\item[(e)] (4)  How many points of inflection does $y = f(x)$ have in the interval
$[-4,4]$, and what are the approximate $x$-values where they are located? 
\item[] Answer: $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
\end{enumerate}
\end{enumerate}
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