Hooke’s law is applicable to idealized (linear) springs that are not stretched or compressed too far. Consider a nonlinear spring whose restoring force is given by 

F(x) = 16x - 0.1x³, for |x| ≤ 7.

a. Graph the restoring force and interpret it.

b. How much work is done in stretching the spring from its equilibrium position (x = 0) to x = 1.5?

c. How much work is done in compressing the spring from its equilibrium position (x = 0) to x = -2?