Consider a spring that does not obey Hooke’s law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with x-component Fx=kx−bx2+cx3 must be applied to the free end. Here k = 100 N/m, b=700N/m2, and c=12,000N/m3. Note that x < 0 when the spring is stretched and x > 0 when it is compressed. How much work must be done

(a) to stretch this spring by 0.050 m from its unstretched length?
(b) To compress this spring by 0.050 m from its unstretched length?
(c) Is it easier to stretch or compress this spring? Explain why in terms of the dependence of Fx on x. (Many real springs behave qualitatively in the same way.)