A force is given by F_x = Ax^-3, where A = 8 N•m³.

(a) For positive values of x, does the potential energy associated with this force increase or decrease with increasing x? (You can determine the answer to this question by imagining what happens to a particle that is placed at rest at some point x and is then released.) 

(b) Find the potential-energy function U associated with this force such that U approaches zero as x approaches infinity. 

(c) Sketch U versus x.