Hello Herotutors, please I have a question about a Calculus. In the question I am asked to find the angle between the ropes at the pulley. What I made was to calculate the first derivative to find the maximum point given by the tangent line but I am stock in the process of optimization, please I will appreciate your help.

5. Consider a rope of length if' with a mass W attached at one end, and a pulley attached at the other. 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 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 the system, 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 sin{,r'2] + 2[HIEI d For question 5 Amume the distance V between tbeeeillugandtbe weight is a maximum at equilibrium