A single conservative force vec$(F)=(4\mathrm{.}0x-12)hat(i)N$ where $x$ is in meters, acts on a particle moving along an $x$ axis. The potential energy $U$ associated with this force is assigned a value of $22$ J at $x=0.$

$($a$)$ Write an expression for $U$ as a function of $x,$ with $U$ in joules and $x$ in meters.

$U(x)=$

$($b$)$ What is the maximum positive potential energy?

J

$($c$)$ At what negative value of $x$ is the potential energy equal to zero?

m

$($d$)$ At what positive value of $x$ is the potential energy equal to zero?

m