Question

Responses are graded based on clarity and to the extent to which we have justified our answers. (If clarification of "l" is needed, it is the length of rope starting from point B, passing through the pulley at point F and ending at the weight attached at point D) For context, this problem is from a Calculus 1 course which just covered applications of differentiation including l'Hospital's rule and optimization problems.

One of the problems posed by the Marquis de lđHospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C by a rope of length r. At another point B on the ceiling, at a distance d from C (where d>r), a rope of length is attached and passed through the pulley at F and connected to a weight W. The weight is released and comes to rest at its equilibrium position D. (See the figure.) As lâHospital argued, this happens when the distance ED is maximized. Show that when the system reaches equilibrium, the value of x is 4d Notice that this expression is independent of both W and

Answer 1

Answe 0 ot Probes Posed b> the maot d Hoisito n his Coss fent bookdeg attached to the ceiang oi atom at a Point chy lryth夂 attached and pQcnd-thrash the Ud. we have ct-d, Eccfr and ovn

d-x d거 OA

3 But X20 ud