cusp

Short definition from Wiktionary

Noun

1. 1
   A sharp point or pointed end.
2. 2
   An important moment when a decision is made that will determine future events.
3. 3
   A point of a curve where the curve is continuous but has no derivative, but such that it has a derivative at every nearby point.
4. 4
   A point made by the intersection of two curved lines or curved structures, a common motif in Gothic architecture.
5. 5
   A boundary between zodiacal signs and houses.
6. 6
   Any of the pointed parts of a canine tooth or molar.
7. 7
   A flap of a valve of a heart or blood vessel.
8. 8
   A point of transition.

Verb

1. 1
   To behave in a reckless or dangerous manner.