% HMC Math dept HW template example
% v0.04 by Eric J. Malm, 10 Mar 2005
\documentclass[12pt,letterpaper,boxed]{hmcpset}

% set 1-inch margins in the document
\usepackage[margin=1in]{geometry}

% include this if you want to import graphics files with /includegraphics
\usepackage{graphicx}

% include this to have lists enumerated by letters
\renewcommand{\labelenumi}{(\alph{enumi})}

% info for header block in upper right hand corner
\name{}
\class{Math 315}
\assignment{Homework \#15}
\duedate{6/2/2017}

% macros
\newcommand{\NN}{\mathbb{N}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\II}{\mathbb{I}}

\begin{document}

\problemlist{Abbott: 5.3.7, 5.3.8}


\begin{problem}[5.3.7]
A \emph{fixed point} of a function $f$ is a value $x$ where $f(x) = x$. Show that if $f$ is differentiable on an interval with $f'(x) \neq 1$, then $f$ can have at most one fixed point.
\end{problem}

%\begin{solution}
%
%\end{solution}

\newpage

\begin{problem}[5.3.8]
Assume $f$ is continuous on an interval containing zero and differentiable for all $x \neq 0$. If $\lim_{x \to 0} f'(x) = L$, show $f'(0)$ exists and equals $L$.
\end{problem}

%\begin{solution}
%
%\end{solution}



\end{document}
