Which of the following describes the behavior of the graph
$\displaystyle y=\sqrt[4]{|x-2|}$ at $\displaystyle x=2$?
1. differentiable
2. corner
3. cusp
4. vertical tangent
5. discontinuity
I think its a cusp..but not sure.
Thanks!
The left and right derivatives go to $\displaystyle \mp$ infinity as $\displaystyle x$ goes to $\displaystyle 2$, which in the case of slopes are the same thing (the curve is vertical on both sides at $\displaystyle x=1$) which of course makes the point a cusp.
CB