Potential energy always tends to minimize itself. This characteristic of potential energy leads to two types of equilibrium positions. If the equilibrium position is local minimum, such as a valley between two hills, the equilibrium is stable. If the object is displaced from this position and then allowed to move freely, the object will return to this equilibrium position. If the object is at rest somewhere other than a local minimum, the equilibrium is unstable. For example, an object at rest on top of a hill is in an unstable equilibrium. If it is displaced and allowed to move freely, it will travel down the hill, but it will not return to the top. The potential energy is less at the bottom of the hill than at the top, so, if the ball remains at the bottom of the hill after being displaced from the top, it is actually minimizing potential energy, as required. All that is required for the point to be a stable equilibrium is that the point be a local minimum.
