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\begin{center}
{\Large TEST 2

Math 2210}
\end{center}

\begin{itemize}
\item  You have 1 hour to complete this exam.
\item  Show all your work (and make it neat!).  
  If I can't follow your work or it is missing you WILL NOT get credit.
\item  You can use a $4 \times 6$ note card of notes.
\item  If you run out of space, use the back of these sheets.
\end{itemize}


\vspace{.4in}

Name: \hrulefill


\begin{enumerate}


\item (10 points) For the surface defined by $z=x^2-xy-2y^2$, find the equation of the tangent plane at the
  point $(1,2,-9)$.


\item  (10 points) Consider the function $f(x,y,z)=x^2-3xy-yz$.
  \begin{enumerate}
  \item  In what direction is $f$ decreasing most rapidly at the point $(2,1,1)$?
  \item  What is the directional derivative of $f$ at $(2,1,1)$ in the direction $(1,3,4)$?
  \end{enumerate}

\item  (10 points) Find all extrema and saddle points for the function $f(x,y)=x^2y-6y^2-3x^2$.

\item  (10 points) Consider the double integral below:
  \[
  \int_0^2 \int_{-2y}^{y/2} \; dx\; dy
  \]
  \begin{enumerate}
  \item  Draw the region of integration in the $xy$-plane.
  \item  Rewrite the integral by switching the order of integration.
    \\
    (Hint: this may require writing the integral down as two integrals.)
  \item  Evaluate the integral.
  \end{enumerate}




\end{enumerate}

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