\input{ThisWeek.tex}
\newcommand{\classday}{\Thursday}
\input{../TemplateWeek/InClassWork.tex}
\input{Exercises.tex}

%\booltrue{teacher}

%This one was a struggle.  
%The first warmup is confusing because we switch linearizations.  This might be worth it, but might not be
%A lot of people struggled even with the warm-up; those shouldn't be this hard
%Basically no one had the relevant formulas about relative error and so on, or remembered that they were supposed to
%Also a lot of people don't understand the concept.  Not sure what to do about that.

\section*{Warm Up}
\begin{enumerate}[label=(\alph*)]
\item \Exercise{E3-11_WarmUp1}
\item \Exercise{E3-11_WarmUp2}
\end{enumerate}
\pagebreak
\section*{Exercise 1}
\Exercise{E3-11_Main1}

\section*{Exercise 2}
\Exercise{E3-11_Main3}

\section*{Exercise 3}
\Exercise{E3-11_Main4}

\section*{Exercise 4}
\Exercise{E3-11_Main5}

\section*{Exercise 5}
\Exercise{E3-11_Main6}

\section*{Exercise 6}
 Consider this graph of points satisfying $y^2=x^3-x+\sqrt{\frac{4}{27}}$:

\begin{tikzpicture}
  \begin{axis}[width=240, height =200, xmax=2, ymax=2, xmin=-2, ymin=-2, xlabel=$x$, ylabel=$y$, axis x line = middle, axis y line=middle]
\addplot[smooth,samples=1000,domain=-1.1547:1.75] gnuplot{sqrt(x**3-x+2*sqrt(1./27))};
\addplot[smooth,samples=1000,domain=-1.1547:1.75] gnuplot{-sqrt(x**3-x+2*sqrt(1./27))};
  \end{axis}
\end{tikzpicture}

\begin{enumerate}[label=(\alph*)]
\item Before taking the derivative, use the graph to identify where you think the derivative of this curve will be defined.
\item Use implicit differentiation to find the derivative $\frac{dy}{dx}$?  (Your final answer should be $\frac{dy}{dx}=\cdots$ with only $x$ and $y$ on the right.)
\item Compare the points where $\frac{dy}{dx}$ isn't defined to the points on the curve where you didn't expect the derivative to be defined.
\item Use implicit differentiation to find the derivative $\frac{d^2y}{dx^2}$.   (Your final answer should be $\frac{d^2y}{dx^2}=\cdots$ with only $x$ and $y$ on the right.)
\end{enumerate}


\end{document}

