Actually the following question came in an exam i gave yesterday. I know the site does not allow home-work type questions, but as I am having a conceptual problem in solving the question, I am posting it anyway. The question is:
A particle is acted upon by a force given by $F= -ax^3 -bx^4$ where $a$ and $b$ are positive constants. At point $x=0$, the particle is $1)$ in stable equilibrium$/ 2.) $in unstable equilibrium$/ 3.)$in neutral equilibrium$/4.)$ not in equilibrium. Which option is correct.
My question how to figure out from the force-displacement equation, whether a particle is in equilibrium or not and in what type of equilibrium. I guess it has something to do with potential energy but cannot figure it out.