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.