\begin{frame}
  \frametitle{Newton's Method}
  
  \begin{center}
  \scalebox{.8}{
  \begin{tikzpicture}[default,baseline=1cm]
    \diagram{-.5}{4}{-.5}{4}{1}
    \diagramannotatez
    \begin{scope}[ultra thick]
      \draw[cgreen,ultra thick] plot[smooth,domain=-0:3.3,samples=200] function{-.5 + (.5*x)**3};
      \node[include=cgreen] (r) at (1.58,0) {};
      \node[anchor=south east] at (r) {$r$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}
  \pause
  
  Assume we want to find a root of a complicated function like:
  \begin{talign}
    f(x) = x^{7} - x + \cos x
  \end{talign}
  \pause
  Often it is impossible to solve such equations!
  \pause
  E.g. there are no formulas for solutions of polynomials of degree of $\ge 5$.
  \pause

  \begin{exampleblock}{}
    Can we at least find the root approximately?  
  \end{exampleblock}
  \vspace{10cm}
\end{frame}