The magnitude of the gravitational force between two objects of mass M and m is given by F(x) = -GMm/x², where x is the distance between the centers of mass of the objects and G = 6.7 × 10^-11 N-m^2/kg² is the gravitational constant (N stands for newton, the unit of force; the negative sign indicates an attractive force).

a. Find the instantaneous rate of change of the force with respect to the distance between the objects.

b. For two identical objects of mass M = m = 0.1 kg, what is the instantaneous rate of change of the force at a separation of x = 0.01 m?

c. Does the instantaneous rate of change of the force increase or decrease with the separation? Explain.