Question #2b0d7

1 Answer
Oct 18, 2014

Remember that differentiability ensures the smoothness of the graph of a function, so if there is a sharp corner in the graph, then the function is not differentiable there.

Let us look at the graph of #y=|x|# below.

enter image source here

As shown above, #y=|x|# is differentiable on #(-infty,0)cup(0,infty)# since it is just a part of a straight line; however, it is not differentiable at #x=0# since there is a sharp corner there.


I hope that this was helpful.