\begin{frame}
  \frametitle{2nd Midterm Exam - Review}
  
  \begin{exampleblock}{}
    Show that $f(x) = 2e^x + 3x + 15x^3$
    has no tangent with slope $2$.
    \pause\bigskip

    We have:
    \begin{align*}
      f'(x) = 2e^x + 3 + 5x^2
    \end{align*}
    \pause
    Note that
    \begin{align*}
      e^x \ge 0 &\quad\text{ for all $x$}\\
      \mpause[1]{x^2 \ge 0} &\mpause[1]{\quad\text{ for all $x$}}
    \end{align*}
    \pause\pause
    and thus
    \begin{align*}
      f'(x) = 2e^x + 3 + 15x^2 \ge 3
    \end{align*}
    \pause
    The slope of the curve $f(x)$ is $\ge 3$ everywhere.\\\pause
    Hence the curve cannot have a tangent with slope $2$. 
  \end{exampleblock}
\end{frame}