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\begin{frame}
\frametitle{Mean Value Theorem}

\meanvalue

\only<3>{
\begin{center}
\scalebox{.8}{
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-.5}{4}{-.5}{3.5}{1}
\diagramannotatez
\draw[gray] (.5,2) -- node [black,at end,below] {$a$} (.5,-.2);
\draw[gray] (3.5,1) -- node [black,at end,below] {$b$} (3.5,-.2);
\draw[gray] (2,2.5) -- node [black,at end,below] {$c$} (2,-.2);
\begin{scope}[ultra thick]
\draw[cgreen,ultra thick] (.5,2) to[out=45,in=180-19.47] (2,2.5) to[out=0-19.47,in=130] (3.5,1);
\end{scope}
\draw[cblue] (.5,2) -- (3.5,1);
\node (a) at (2,2.5) {};
\draw[cred] ($(a)+(-1.5,1.5/3)$) -- +(3,-3/3);
\end{tikzpicture}
}\hspace{1cm}
\scalebox{.8}{
\begin{tikzpicture}[default,baseline=1cm]
\diagram{-.5}{4}{-.5}{3.5}{1}
\diagramannotatez
\draw[gray] (.5,1) -- node [black,at end,below] {$a$} (.5,-.2);
\draw[gray] (3.5,3) -- node [black,at end,below] {$b$} (3.5,-.2);
\draw[gray] (1.3,2.5) -- node [black,at end,below] {$c_1$} (1.3,-.2);
\draw[gray] (2.8,1.5) -- node [black,at end,below] {$c_2$} (2.8,-.2);
\begin{scope}[ultra thick]
\draw[cgreen,ultra thick] (.5,1) to[out=45+30,in=180+30] (1.3,2.5) to[out=0+30,in=180+30] (2.8,1.5) to[out=0+30,in=-100] (3.5,3);
\end{scope}
\draw[cblue] (.5,1) -- (3.5,3);
\node (a) at (1.3,2.5) {};
\draw[cred] ($(a)+(-1.5,-1.5/2)$) -- +(3,3/2);
\node (a) at (2.8,1.5) {};
\draw[cred] ($(a)+(-1.5,-1.5/2)$) --  +(3,3/2);
\end{tikzpicture}
}
\end{center}
}
\pause

\vspace{10cm}
\end{frame}