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\noindent {\bf Problem statement} The amount of a substance which can
be dissolved in a solution may vary with temperature. Below is a graph
of the solubility (the maximum amount of the substance) in grams of
sodium sulfate, $\rm Na_2SO_4$, which can be dissolved in 100 grams of
water as a function of temperature in degrees Celsius. Suppose $S(T)$
is the solubility at temperature $T$. Use the graph to answer the
following questions as well as you can.

%This information is obtained from Linke, W.F.; A. Seidell
%(1965). Solubilities of Inorganic and Metal Organic Compounds, 4th
%edition, Van Nostrand.

\centerline{\epsfxsize=3.75in\epsfbox{w1F.eps}}


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\noindent a) Where is $S(T)$ continuous? Where is $S(T)$
differentiable?
 
\medskip

\noindent b) Where is $S(T)$ increasing? Where is it decreasing? Does
$S(T)$ have any local extrema? If yes, where and what type?

\medskip

\noindent c) In what intervals is $S(T)$ concave up? In what intervals
is $S(T)$ concave down? Does $S(T)$ have any points of inflection?

\medskip

\noindent d) Sketch a graph of $S'(T)$. What are the units on each
axis of your graph?

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