A particle free to move along the x-axis has potential energy given by $\mathrm{U}\left(\mathrm{x}\right)=\mathrm{k}\left[1-\exp \left(-{\mathrm{x}}^2\right)\right]\text{ for }-\mathrm{\infty }\le \mathrm{x}\le +\mathrm{\infty }$ where k is a positive constant of appropriate dimensions . Then

if its total mechanical energy is k/2 it has its minimum kinetic energy at the origin.

for small displacements from x =0 , the motion is SHM

at points away from the origin, the particle is in unstable equilibrium

for any finite non-zero value of x, there is a force directed away from the origin