A particle free to move along the x -axis has potential energy given by U(x)=k[1−exp(−x2)] for −∞≤x≤+∞ , 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 nonzero 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