Exit Sign Problem: The base of a 20-ft-tall exit sign is 30 ft above the drivers eye

Chapter 4, Problem 26

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Exit Sign Problem: The base of a 20-ft-tall exit sign is 30 ft above the drivers eye level (Figure 4-5i). When cars are far away, the sign is hard to read because of the distance. When they are very close, the sign is hard to read because drivers have to look up at a steep angle. The sign is easiest to read when the distance x is such that the angle at the drivers eye is as large as possible. Figure 4-5i a. Write as the difference of two inversecotangents.b. Write an equation for d / dx.c. The sign is easiest to read at the valueof x where stops increasing and startsdecreasing. This happens when d /dx = 0.Find this value of x.correct, plot as a function of x and thusshow that the graph really does have a highpoint at that value.