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\noindent {\bf Problem statement} Consider the functions given by the
equation $f_c(x)=(x^2+c)e^x$, where $c$ is a parameter.

\medskip

\noindent a) Use the calculator to observe the curves for the values
$c=0,1,2$ when $x$ is in the interval $[-4,1]$. Do all three curves
have the same number of horizontal tangents? Do all three curves have
the same number of inflection points? You may have to {\it zoom}\/ in
to investigate this.

\medskip

\noindent b) Use calculus to determine the location of all the
inflection points of the graph of $y=f_c(x)$. Your answer may depend
on $c$.

\medskip

\noindent c) At what values of $c$ does the number of inflection
points change?  What are the values of $c$ (if any) for which there is
exactly one inflection point?

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