The potential energy of a particle moving along the x axis is U = 2x² - 6x joules, with x in metres…

Step 1. Force. $F = -\dfrac{dU}{dx} = -(4x - 6)$. At $x = 3\ \text{m}$: $F = -6\ \text{N}$, pointing toward $-x$.

Step 2. Equilibrium. $F = 0$ when $4x - 6 = 0$, that is $x = 1.5\ \text{m}$.

Step 3. Stable? $U$ is a parabola opening upward, so $x = 1.5\ \text{m}$ is its minimum: the equilibrium is stable.