\documentclass{article}

\usepackage[usenames,dvipsnames]{color,xcolor}

\usepackage{tikz}
\usetikzlibrary{mindmap,backgrounds,shadows,trees,positioning,shapes,arrows,decorations,calc,shapes,intersections,arrows,decorations.pathreplacing}


\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1mm}

%\usepackage{fontspec}
%\setmainfont[Scale=.8]{Linux Libertine}


\begin{document}
\begin{tikzpicture}


\coordinate (a) at(1,6);
\coordinate (b) at(10,4);

\draw[dashed](a)-- ++(0,-6) node[at end,below]{a};
\draw[dashed](b)-- ++(0,-4)node[at end,below]{b};



\draw[dashed](8.5,1.7)--(8.5,0)node[at end,below]{$x_{0}$};
\draw[dashed](8.5,1.7)--(0,1.7)node[at end,left]{$k$};

\draw[-latex](0,0)--(11,0) node[below]{$x$};
\draw[-latex](0,0)--(0,7)node[left]{$y$};

\draw [] (a)..controls (2,4) and (3,4) .. (4,5)
..controls (5,6) and (6,6)..(7,3.5)
..controls (8,1) and (9,1)..(b);


\draw[fill=black](a)circle(.4mm);
\draw[fill=black](b)circle(.4mm);




\end{tikzpicture}
\end{document}