A particle moving along the x-axis has potential energy U(x) = k[1 − exp(−x²)], where k > 0. Which statement is correct?

Options

• Option A

  at point away from the origin, the particle is in unstable equilibrium.

• Option B

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

• Option C

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

• Option D

  for small displacements from x = 0, the motion is simple harmonic.