momentum, momentum

The potential energy of an object constrained to move in the x-direction is given by U(x) = a x^4 + b x^2, where
a = 24 J/m4 and b = -7.0 J/m2.
Find the equilibrium points and state whether they are stable or unstable

U(x) = a x^4 + b x^2

I have a few questions:

is "a" acceleration or not?

also does the object move in a straight line or not?

I would try to answer if u can just get these two cleared for me and can you give me the context in which this question was asked? (or perhaps the exact phrasing)

U(x) = a x^4 + b x^2

IN the problem a is represented as the infinity sign and b is represented as the alpha sign. I didn't know how to type that so I just put a and b. It told me to "Give your answers in order of increasing value of |x|"

Maybe it moves in a straight line. i don't know

Sorry - I've had a few drinks and this thread cheered me up from the start.
Drude - checking your PM is more important than answering this.

so can anybody help me

ok, I drew the picture and it looks symmetrical but what do you mean by equilibrium point?

isn't this just finding critical points i.e. when U'(x)=0?

yes, that crossed my mind but what is equilibrium point. I mean in case it is the critical point then ya just have him differentiat it and put it equal. He can even do the U'' to investigate teh functions cavity and etc. But I mean in physics equilibrium is involved with force.....I dont recall seeing potential energy used as such.