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 F. = kx - bx2 + cx3 must be applied to the free end. Here k = 100 N/m, b = 700 N/m2 , and c = 12,000 N/m3. Note that x > 0 when the spring is stretched and x < 0 when it is compressed. (a) How much work must be done to stretch this spring by 0.050 m from its unscratched length? (b) How much work must be done to compress this spring by 0.050 m from its unscratched length? (c) Is it easier to stretch or compress this spring? Explain why in terms of the dependence of F. on x. (Many real springs behave qualitatively in the same way.)