\documentclass{article}[11 pts] 

\begin{document}

\centerline{\bf ADVANCED CALCULUS, Math 127 B}
\centerline{\bf Homework 7 Due March 12}
\vskip 5pt

\begin{enumerate}

\item If $f(0,0)=0$ and $f(x,y)=\frac{xy}{x^2+y^2}$ otherwise. Prove
that the partial derivatives with respect to $x$ and $y$ exist at every
point, although $f$ is not continuous at $(0,0)$.

\item If $f$ is a differentiable mapping of a connected set $E \subset R^n$
and if $f$ has a local maximum at a point $x \in E$, prove that $f'(x)=0$.

\item 6.13, 6.20, 6.24

\end{enumerate}

\end{document}
