A child is swinging back and forth on a swing. Changes in her kinetic and potential energy are happening each moment. At which point or multipoint in her swinging would each of these two types of energy be at a maximum?

The kinetic energy of the child would be at a maximum at the lowest point of the swing, when she is moving at her fastest speed. The potential energy of the child would be at a maximum at the highest point of the swing, when she is at her greatest height above the ground.