The rope is suspended from two books [a distance d' apart}, and the weight is pamed through the pulleyr [see gure below}. Aer the weight is released...

Hello dear tutors, I hope you can give support to this exercise of Calculus. I have already found the answer for the first step using the principles of triangles, but I am stuck in the final resolution to find the maximum equilibrium, do I need to use the first and second derivatives? could you explain how to determine that part of the problem? thanks for your help, I appreciate it. 

5. Consider a rope of length if' with a mass W attached at one end, and a pulley attached at the other. Therope is suspended from two books [a distance d' apart}, and the weight is pamed through the pulleyr [see figurebelow}. Afler the weight is released and comes to equilibrium, determine the angle between ropes at the pulley,6', assuming that the distance between the weight and the ceiling is a maximum. From the symmetry of thesystem, you can assume that the weight comes to rest half-way between the hooks. Hint: First show that the _ . 1 .- . . _ _ _ d '5‘:distance of the weight from the oeibng [5 given by L09} — f d s—in{fl,r’2] + 2—[HIEI—d— For question 5 — Amume the distance Vbetween tbeeeillugandtbe weight is a maximum at equilibrium.