At $x=x_0$, a smooth potential energy graph has a horizontal tangent, with negative slope immediately to the left of $x_0$ and positive slope immediately to the right of $x_0$. Which statement is correct?

$x_0$ is an equilibrium candidate and the force points toward $x_0$ on both sides

The force is zero everywhere near $x_0$ because the tangent is horizontal at one point

$x_0$ is not an equilibrium candidate because the slope changes sign

$x_0$ is an equilibrium candidate and the force points away from $x_0$ on both sides