Define conservative forces. What are the properties of conservative forces?

The potential energy $U$ between two molecules as a function of distance $x$ between them is shown. $A, B, C$ are points for which $x = 0.6 \mathring{A}, 1.2 \mathring{A}, 1.8 \mathring{A}$ respectively. At $A, B, C$,the force between the two molecules is:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: In a central force field,the work done is independent of the path chosen.
Reason $R$: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements,choose the most appropriate answer from the options given below:

If $F = 2x^2 - 3x - 2$,then choose the correct option.

In a gravitational field,if the work done along paths $1, 2$ and $3$ is ${W_1}, {W_2}$ and ${W_3}$ respectively,then:

The potential energy of an object of mass $m$ moving in the $xy$ plane in a conservative field is given by $U = ax + by$,where $x$ and $y$ are position coordinates of the object. Find the magnitude of its acceleration.