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A particle free to move along the x-axis...

A particle free to move along the `x-`axis has potential energy given by `U(x) = k[1 - e^(-x^(2))]` for `-oo le x le + oo`, where `k` is a positive constant of appropriate dimensions. Then select the incorrect option

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.

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