Two vertical towers (PQ and ST) are secured by a steel cable. The cable goes from the top of one tower (P), to a point on the ground between the towers (R), to the top of the other tower (T). Assume that the height of tower is double the height of the other. Find the position of R that requires the least amount of cable. Calculate the minimal cable length. (Adapted from Calculus 4th Ed. (Stewart, p. 285, item 48)).

Find a function of the total length of cable with respect to the length of segment QR. Plot the graph. Point M should trace your graph (if it doesn't, you'll need to revise your function). Once you have a working graph, explore relationships between QR and minimum cable length for various tower heights. What patterns do you see?