Cusp (noun)

1. A sharp or pointed end or apex.
2. A turning point or decisive moment.
3. A point where two curves meet and change direction.

Origin:

Late middle english: from latin cuspis "point, spearhead".

Examples:

1. The mountain had a cusp that offered a breathtaking view.
2. The election was on the cusp of a historic change.
3. The cusp of the waves was white with froth.
4. The cusp of the arch was beautifully decorated.
5. The cusp of the leaves was a delicate shade of green.