Principle of total minimum Potential Energy

Hence, if these curves represent the actual paths of a particle, one can see that the particle can be at equilibrium at the designated points in the path. One can observe the difference in the types of equilibrium. In the left most curve, the particle is at stable equilibrium at the marked point. That means if we disturb a particle from the position of equilibrium, it tries to come back to the point.

In the middle curve, though the particle can be in equilibrium at the topmost point, any disturbance will cause the particle to move away from the position of equilibrium. Thus if the variation of potential energy is zero, but the potential energy is maximum, the system is in unstable equilibrium.

In the rightmost curve, the point is the point of inflection, and is neither minimum nor maximum. Cyrvature on both side of the point is different. Here also the particle will be in unstable equilibrium, since any displacement to the left of the equilibrium configuration will result in an increasing departure from the position.