A particle free to move along the x-axis has potential energy given by U(x) = K[1-exp(-x2)]  for -∞ < x< +∞ where t is a positive constant of appropriate dimensions. Then

Since F = -dUdx = 2kx exp(-x2)F = 0 (at equilibrium as x = 0)U is minimum at x = 0 and Umin = 0U is maximum at x →±∞ and Umax = kThe particle would oscillate about x = 0 for small displacement from the origin and it is in stable equilibrium at the origin.