An object moving on a one-dimensional line is subject to a force. The force is conservative and the associated potential energy function is $$U(x) = x^4 - 2x^2$$ Find the force vector.
The force vector for this potential function should be $\vec{F} = 4x^3 - 4x$, but if you examine their graph,
we can see that the force vector doesn't always point the lowest energy point, i.e equilibrium point.So, what is the problem ? I mean physically, the force vector must always be in the direction of the lowest energy.Note that the function that is in the shape of reverse M is the potential function.