A model potential for motion along a track is $U\left(x\right)=a{x}^3+b{x}^2+c$, where $a$ and $b$ are constants. Which expression gives the force and correctly identifies the role of $c$?

$F\left(x\right)=-(3ax+2b)$, and $c$ changes the equilibrium positions

$F\left(x\right)=-a{x}^3-b{x}^2-c$, and $c$ reverses the force direction

$F\left(x\right)=3a{x}^2+2bx$, and $c$ adds a constant force

$F\left(x\right)=-(3a{x}^2+2bx)$, and $c$ does not affect the force