Think of it as taking it both ways. :shock:

No seriously. Imagine a function. Then, anything below the x-axis is reflected above it. So, take |x|.

If y = x, at -1, y = -1.

If y = |x|, at -1, ordinarily y should equal -1. But as all negative y values are reflected in the x-axis, thus y = 1 instead. Instead of a straight line graph, you get a sorta V shaped graph.

The graph is defined separately - so for y = |x|, for domain (-infinity, 0] the equation is -x. For domain (0,infinity), the equation is x.

Incidentally, there is no derivative at cusps, or sharp points. Usually, it is at the x-intercepts the derivative is not defined, but check the graph just in case. If it looks sharp, it ain't defined. Open circles.