Verify that the equation F (x, y) = 0 near the point (x0, y0) = 1 to unloading is in the form y = ? (x), and give the second order Taylor Approach for ? around x0 = 1.
This comes across as a raw homework problem, which is not appropriate for this forum.
At least translate it into Wolfram Language. Basic tutorials are at http://reference.wolfram.com/mathematica/tutorial/GettingStartedOverview.html