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

• A
  At points away from the origin,the particle is in unstable equilibrium
• B
  For any finite non-zero value of $x$,there is a force directed away from the origin
• C
  If its total mechanical energy is $k/2$,it has its minimum kinetic energy at the origin
• D
  For small displacements from $x = 0$,the motion is simple harmonic