Copyright © University of Cambridge. All rights reserved.
'Slide' printed from http://nrich.maths.org/
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.