The points on a medium that move up and down with the largest amplitude in a standing wave are called antinodes.

Here's why:

* Standing Waves: Standing waves are formed when two waves of equal frequency and amplitude interfere with each other while traveling in opposite directions.

* Nodes: At certain points along the medium, the waves interfere destructively, resulting in zero amplitude. These points are called nodes.

* Antinodes: At other points, the waves interfere constructively, resulting in maximum amplitude. These points are called antinodes.

So, antinodes are the points of maximum displacement and energy in a standing wave.