The potential energy of a body of mass m is given by U(x) = -mgx + 1/2kx^2. The corresponding force is​

 F = (mg - kx)  i ^

Explanation:

Force and potential are related

         F = - ( i ^ + \frac{dU}{dy} j ^ + \frac{dU}{dz} k ^)

in this exercise we are told that the potential is

         U = - m g x + ½ kx²

let's make the drive

         \frac{dU}{dx} = -mg + kx

         \frac{dU}{dy}= 0

          \frac{dU}{dz} = 0

we substitute

         F = (mg - kx)  i ^

conservation of mass

mass before something happens = mass afterwards