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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.