\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[scale=0.7, every node/.style={scale=0.7}]
  \draw[->] (0, 0) -- (5.2cm, 0) node[right] {$t$};
  \draw[->] (0, 0) -- (0, 5.2cm) node[above] {$s(t)$};

  % Mark the x_1, ..., x_4 points.
  \foreach \x in {1, ..., 4}
    \draw (\x, 0pt) node[below] {$t_{\x}$} -- (\x, 1pt);

  % Point (x_1, y_1), dashed line downwards, dashed line leftwards.
  \draw[thick, black, fill=black] (1cm, 1.5cm) circle (0.2mm);
  \draw[dashed] (1cm, 0cm) -- (1cm, 1.5cm);
  \draw[dashed] (0cm, 1.5cm) node[left] {$s_1$} -- (1cm, 1.5cm);

  % Point (x_2, y_2), dashed line downwards, dashed line leftwards, and full
  % line from point (x_1, y_1).
  \draw[thick, black, fill=black] (2cm, 1.9cm) circle (0.2mm);
  \draw[dashed] (2cm, 0cm) -- (2cm, 1.9cm);
  \draw[dashed] (0cm, 1.9cm) node[left] {$s_2$} -- (2cm, 1.9cm);
  \draw[-] (1cm, 1.5cm) -- (2cm, 1.9cm);

  % Point (x_3, y_3), dashed line downwards, dashed line leftwards, and full
  % line from point (x_2, y_2).
  \draw[thick, black, fill=black] (3cm, 2.7cm) circle (0.2mm);
  \draw[dashed] (3cm, 0cm) -- (3cm, 2.7cm);
  \draw[dashed] (0cm, 2.7cm) node[left] {$s_3$} -- (3cm, 2.7cm);
  \draw[-] (2cm, 1.9cm) -- (3cm, 2.7cm);

  % Point (x_4, y_4), dashed line downwards, dashed line leftwards, and full
  % line from point (x_3, y_3).
  \draw[thick, black, fill=black] (4cm, 4.0cm) circle (0.2mm);
  \draw[dashed] (4cm, 0cm) -- (4cm, 4.0cm);
  \draw[dashed] (0cm, 4.0cm) node[left] {$s_4$} -- (4cm, 4.0cm);
  \draw[-] (3cm, 2.7cm) -- (4cm, 4.0cm);

  % Text below the graph.
  \node[align = center, above] at (2.5cm, -1cm) {$t_2 - t_1 = t_3 - t_2 = t_4 - t_3$};

  % Interpolated smooth graph, touching at points (x_1, y_1), ..., (x_4, y_4).
  \draw [magenta, ultra thin] plot [smooth] coordinates {(0.8cm, 1.3cm) (1cm, 1.5cm) (2cm, 1.9cm) (3cm, 2.7cm) (4cm, 4.0cm) (4.2cm, 4.5cm)};
\end{tikzpicture}
\end{document}