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\noindent {\bf Problem statement} For any constant $c$, define the
function $f_c$ with the formula $f_c(x) = x^3 + 2x^2 + cx$. 

\medskip

\noindent a) Graph $y=f_c(x)$ for these values of the
parameter $c$: $c= -1, 0, 1, 2, 3, 4$. What are the similarities and
differences among the graphs, and how do the graphs change as the
parameter increases?

\medskip

\noindent b) For what values of the parameter $c$ will $f_c$ have one
local maximum and one local minimum? Use calculus. As $c$ increases,
what happens to the distance between the local maximum and the local
minimum?

\medskip

\noindent c) For what values of the parameter $c$ will $f_c$ have no
local maximum or local minimum? Use calculus.

\medskip

\noindent d) Are there any values of the parameter $c$ for which $f_c$
will have exactly one horizontal tangent line?

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