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\begin_body

\begin_layout Itemize

The 
\begin_inset Formula $y$
\end_inset

 values should be larger than 
\begin_inset Formula $\ec m$
\end_inset

, because 
\begin_inset Formula $\ec m$
\end_inset

 is a minimum. 
\end_layout

\begin_layout Itemize

If 
\begin_inset Formula $\ec x<c$
\end_inset

 but close to 
\begin_inset Formula $\ec c$
\end_inset

, the slopes of the secant lines will be negative:
\begin_inset Formula \[
		\ec\frac{f(x)-f(c)}{x-c}=\frac{\mathrm{positive}}{\mathrm{negative}}
	\]
\end_inset

so the slopes of the tangent lines should also be negative. Thus the derivative should be negative for 
\begin_inset Formula $\ec x<c$
\end_inset

. 
\end_layout

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\backslash
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{
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Extrema: Certainty of computation
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}
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\end_inset

 Think about what must happen to the 
\begin_inset Formula $y$
\end_inset

 values around a minimum 
\begin_inset Formula $\ec m=f(c)$
\end_inset

 at 
\begin_inset Formula $\ec x=a$
\end_inset

. 
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placement h!
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	filename figures/x_ex_right_decreasing.png
	scale 20

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