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\centerline{MATH 133 -- Calculus with Fundamentals 1}
\centerline{Quiz 6 -- November 5, 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 but not any graphing features.  
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\noindent
{\it Questions}
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\begin{enumerate}
\item[(a)]  (5)  State the product rule for differentiating $f(x)g(x)$.
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\item[(b)]  (5) Use the product rule to differentiate $(x^3 + 4x)(e^x - 5x^2)$.    
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\item[2)] 
\begin{enumerate}
\item[(a)] (5) Find the derivative using the quotient rule (no simplification needed yet). 
$$f(x) = \frac{x^3 + 2x + 4}{x^{1/2}}$$
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\item[(b)] (4) It is possible to rewrite $f(x)$ as $f(x) = x^{5/2} + 2x^{1/2} + 4x^{-1/2}$
by dividing the $x^{1/2}$ into each term on the top.  Differentiate this form.
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\item[(c)] (1)  Show that your answers in parts (a) and (b) are equivalent by simplifying
the answer from (a). 
\end{enumerate}
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\begin{figure}
\centering
  \subfloat[Plot A]{\includegraphics[width=70mm]{P1.png}}
  \subfloat[Plot B]{\includegraphics[width=70mm]{P2.png}}
\caption{Plots for Problem 3}
\end{figure}
\item[3)] 
\begin{enumerate}
\item[(a)] (6) Differentiate and simplify:  $f(x) = \displaystyle{\frac{x^2}{x^2 + 1}}$ 
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\item[(b)] (4) One of the two plots above is $y = f(x)$ and the other is $y = f'(x)$ 
for the $f(x)$ from part (a).  Which is which?  Plot A is $\underline{\qquad\qquad\qquad}$ and
Plot B is $\underline{\qquad\qquad\qquad}$
\end{enumerate}
\end{enumerate}
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