\documentclass[12pt]{newtest}
\usepackage{amsmath}
\testdate{17 June 09}
\course{Math 896-503}
\header{Assignment \# 6}
\instructions{Due: June 22nd}

\newcommand{\ii}{\vec{\imath}}
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\newcommand{\ep}{\epsilon}
% \newcommand{\det}{\hbox{det}\,}
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\newcommand{\dlim}{\lim\limits}
\newcommand{\pder}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\ppder}[2]{\frac{\partial^2 #1}{\partial #2^2}}



\newcommand{\extra}{\textsc{Extra Credit:}\,\,}
\newcommand{\hint}{\textsc{Hint:}\,\,}
\newcommand{\bhint}{\\ \hint}


\begin{document}
\question{
Let $f: (a,b) \to \bR^3$ be a regular, twice differentiable curve.
Show that
\[ \kappa = \frac{\|f' \times f''\|}{\|f'\|^3}. \]
\hint Let $g$ be a unit-speed reparameterization of $f$ and
write $f'$ and $f''$ in terms of $g'=T$, $g''=\kappa N$,
the speed function $t \mapsto \|f'\|$ and its derivatives.
}{
}

\end{document}
