Difference quotient

Note: Requires the development version of PGF due to the use of the spy library.

Edit and compile if you like:

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DIFFERENCE QUOTIENT                            %
% Author: Peter Kint                             %
% Date: 28 dec 2009                              %
% Using some PGF/TikZ features like              %
%      'layer'                                   %
%      'decorate'                                % 
%       and the wonderful new 'spy'-feature      % 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Note: This example requires PGF > 2.0 or a recent
% development version of PGF.
\documentclass{article}
\usepackage{pgf,tikz}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}%
\usepackage{pgfplots}
\usetikzlibrary{spy}
\usetikzlibrary{backgrounds}
\usetikzlibrary{decorations}
\date{}
\begin{document}
\pagestyle{empty}
%
% declare extra background layer, (main = default)
\pgfdeclarelayer{background layer}
\pgfsetlayers{background layer,main}
\definecolor{darkgray}{rgb}{0.25,0.25,0.25}
\definecolor{lightgray}{rgb}{0.75,0.75,0.75}
%
\begin{tikzpicture}
    [line cap=round,line join=round,x=2cm,y=2cm,
     %using the 'spy' to magnify a part of the picture
     spy using outlines={rectangle,lens={scale=3}, size=8cm, connect spies},
     %using the decoration 'brace' (=a curly brace as path replacement)
     decoration={brace,amplitude=2pt}]
%main layer
%creating the grid
  \draw [color=lightgray,dash pattern=on 1pt off 1pt, xstep=2cm,ystep=2cm]
 
 
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