Change in potential energy between any two points is defined in terms of the work done by the force in displacing the particle between these two points without any change in kinetic energy.
Potential energy curve : A graph plotted between the potential energy of a particle and its displacement from the centre of force is called potential energy curve. Negative gradient of the potential energy gives force.
If net force acting on a particle is zero, it is said to be in equilibrium.
For equilibrium, dU/dx = 0