\begin{frame}
  \frametitle{The Tangent}

  The \emph{tangent} is a line that touches the curve:
  \begin{itemize}
    \item same direction as the curve at the point of contact
  \end{itemize}

  \begin{center}
  \raisebox{.5cm}{
  \begin{tikzpicture}[default]
    \draw (0,0) circle (1.5cm);
    \begin{scope}[rotate=-50,shift=(0:1.5cm)]
      \draw [red,fill] (0,0) circle (.7mm);
      \draw [red,thick] (0cm,-2cm) -- (0cm,2cm);
    \end{scope}
  \end{tikzpicture}
  }
  \hspace{1cm}
  \scalebox{.7}{
  \begin{tikzpicture}[default]
    \diagram{-1}{5}{-1}{5}{1}
    \draw[name path=x2,ultra thick,cgreen] plot[smooth,domain=-0.25:3.3,samples=20] function{3-2*(x-.9)**2 + (x-.9)**3};

    \node[dot] (P) at (2,{3-2*(2-.9)^2 + (2-.9)^3}) {};
    \node[anchor=south west,at=(P.north)] {$P$};
    \tangent[ultra thick]{80}{80}{3-2*(\x-.9)^2 + (\x-.9)^3}{2}
  \end{tikzpicture}
  }
  \end{center}
\end{frame}