Beamer Ucsandiego

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\title{Improving Low-Resource Neural~Machine~Translation}
\author{Leon Cheung} 
\institute{University of California San Diego}
\date{8 September 2017} % custom date

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\section{What Can Happen at a Critical Point?} 

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\frametitle{The Usual Suspects}

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    jsdf & 0.23 \\
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You might think that if $f'(0)=0$ (and $f$ is not a constant function) then at 
$x=0$, $f$ must have
\begin{itemize}
\pause \item a local maximum, or 
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\begin{frame}
\frametitle{A Counterexample}
\alert{Consider} the function 
\[ 
    f(x)=
\begin{cases} 
x^2\sin(1/x), &\text{if }x\neq0 \\
0, &\text{if }x=0
\end{cases}
\]
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\frametitle{What Really Happens at $x=0$?}
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But $f(x)$ oscillates wildly as $x\to 0$, so even though $f'(0)=0$, $f$ has 
neither max, min, nor inflection point at $x=0$.
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\subsection{What Does $g'(c)>0$ Mean?} 
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\frametitle{What Really Happens at $x=0$?}

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\section{Conclusion}

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The function $f(x)$ introduced earlier has other interesting properties, 
one of which is the fact that while $f'(0)$ exists, $f'(x)$ is 
discontinuous at $x=0$.
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We leave it to you to work this out for yourself and to explore this 
interesting function further.
\vspace{.5cm}

Thank you for your attention today.
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