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\begin{document}

%	\mbox{}
%	\title{Limits and Derivatives (MATH 53)}
%	
%	\maketitle
	

\section*{Directional Derivatives and the Gradient Vector}
\bigskip

\begin{problem}
	Let $f \colon \rr^3 \to \rr$ be a differentiable function, and let $r(t)$, where $t \in [a,b]$, be a parametric curve in the domain of $f$. Show that vectors $\nabla f (r(t))$ and $r'(t)$ are perpendicular for all $t \in [a,b]$.
\end{problem}
	
\vspace{20pt}

\begin{thebibliography}{20}
	
	\bibitem{jS15} J.~Stewart: \emph{Calculus} 8th Edition, Cengage Learning, Boston 2016.
	
\end{thebibliography}
	
\end{document}