Since the tangent does not exist at x = 2 but the curve is continuous, only options 2 and 3 are candidates. But if you look at the definition of each, the answer has to be cusp.
The left and right derivatives go to infinity as goes to , which in the case of slopes are the same thing (the curve is vertical on both sides at ) which of course makes the point a cusp.
CB
Last edited by CaptainBlack; Aug 10th 2009 at 08:19 AM.
Reason: fix typo