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Plot the graph of the function $y=f(x)$ where $f(x) = x(x+|x|)$.
Find the first and second derivatives of the function. Show that
the first derivative exists at $x=0$ but that the second derivative
does not exist at $x = 0$.

NOTES AND BACKGROUND

This is a very simple question but it requires an understanding of
how to handle functions that are defined differently on different
parts of their domains.