Answer
The force is repulsive if the separation is smaller than the equilibrium separation.
Work Step by Step
$U = \frac{A}{r^{12}}-\frac{B}{r^6}$
$\frac{dU}{dr} = \frac{6B}{r^7}-\frac{12A}{r^{13}}$
Suppose that $\frac{dU}{dr} \lt 0$:
$\frac{dU}{dr} = \frac{6B}{r^7}-\frac{12A}{r^{13}} \lt 0$
$\frac{6B}{r^7} \lt \frac{12A}{r^{13}}$
$r \lt \sqrt[6] {\frac{2A}{B}}$
Since $F = -\frac{dU}{dr}$, then $F \gt 0$ when $r \lt \sqrt[6] {\frac{2A}{B}}$
Therefore, the force is repulsive if the separation is smaller than the equilibrium separation.
