\subfloat[Visibility of a point $x$ with respect to $\omega$]{
        \begin{tikzpicture}[domain=-0.5:2]
            \draw[very thin,color=gray] (-0.1,-0.6) grid (2.1,2.1);

            \draw[->] (-0.2,-0.5) -- (2.2,-0.5) node[right] {$\omega$};
            \draw[->] (0,-0.7) -- (0,2.2) node[above] {$V(x,\omega)$};

            \draw (0,0) -- (1,0) plot coordinates {(0,0)  (1,0)}[color=red];
            \draw (1,1) -- (2,1) plot coordinates {(1,1)  (2,1)}[color=red];
            \draw (0,0) node[left] {$0$};
            \draw (0,1) node[left] {$1$};
            \draw (1,-0.7) node[below] {$\omega_0$};
        \end{tikzpicture}
}
\hfil
% second diagram
    \subfloat[Differentiation of the left graph with respect to $\omega$]{
            \begin{tikzpicture}[domain=-0.5:2]
                \draw[very thin,color=gray] (-0.1,-0.6) grid (2.1,2.1);

                \draw[->] (-0.2,-0.5) -- (2.2,-0.5) node[right] {$\omega$};
                \draw[->] (0,-0.7) -- (0,2.2) node[above] {$\frac{\partial}{\partial\omega}V(x,\omega)$};

                \draw (0,0) -- (2,0) plot coordinates {(0,0)  (2,0)}[color=red];
                \draw (0,0) node[left] {$0$};
                \draw (0,1) node[left] {$1$};
                \draw (0,2) node[left] {$\infty$};
                \draw (1,2) node[color=red] {$\bullet$};
                \draw (1,-0.7) node[below] {$\omega_0$};
            \end{tikzpicture}
    }