y=c/x

\documentclass{standalone}
\usepackage[utf8]{inputenc}

\usepackage{tikz}

\begin{document}

\def\n{1}
\def\I{0.7}

\def\II{1.42857}


\begin{tikzpicture}[domain=0:2, xscale=2, yscale=2, >=latex]
  \draw[very thin,color=gray!30] (0,0)
    grid[xstep=0.25, ystep=0.25] (2,2);
  \draw[->, line width=1pt] (0,0) -- (2,0)
    node[below] {$x$};
  \draw[->, line width=1pt] (0,0) -- (0,2)
    node[left] {$y$};
  \draw[color=green!30!black, thick, smooth]
    plot[id=x, domain=0.5:2]
    function{\n/x};
  \draw[dashed, color=gray] (0,0) node[below] {$O$} -- (2,2);
  \node[anchor=base] (vg) at (0.9,1.8)
    {$y = \displaystyle\frac{c}{x}$};
    
  %\draw[->,dashed] (\I,0) node[below] {$x_0$} -- (\I,\II) -- (0,\II)
  %  node[left] {$y_0$};  
    
  %\draw[->,dashed] (\I,0) node[below] {$x_0$} -- (\I,\II) -- (0,\II)
  %  node[left] {$y_0$};  
  \draw[->,dashed]  (\I,\I) --   (\I,\II);
  \draw[->,dashed]  (\I,\II) -- (\II,\II) ;
  \draw[->,dashed]  (\II,\II) -- (\II,\I);
  \draw[->,dashed]  (\II,\I) -- (\I,\I);


  \draw[dashed]  (\I,0) node[below] {$x_0$} --   (\I,\I) -- (\II,\I) -- (\II,0)
    node[below] {$x_1$};
\end{tikzpicture}

\end{document}