Range lights are pairs of lighthouses on bays, rivers, and other waterways that guide boats safely along a linear path, called the range line. Because lighthouses are expensive to build, operate, and maintain, it is reasonable to minimize the number of lighthouses in use by ensuring that the range lines are as long as possible. The portion of a river that is deep enough for boat traffic is referred to as the river's channel. The channel is dredged often to ensure an appropriate depth for safe passage of boats. To keep a boat in a channel bounded by the curves y = f(x) and y = f(x) + h, the optimally long range lines are the secant or tangent lines to the two curves. For example, a boat traveling from left to right on the river shown in figure 1 should stay in the shaded channel.