Chapter 3.7, Problem 299E

[T] A local movie theater with a 30-foot-high screen that is 10 feet above a person’s eye level when seated has a viewing angle $\theta$ (in radians) given by $\theta$

   $\theta ={\cot }^{-1}\frac{x}{40}-{\cot }^{-1}\frac{x}{10}$ . where x is the distance in feet away from the movie screen that the person is sitting, as shown in the following figure.

Find $\frac{d\theta }{dx}$ .

Evaluate $\frac{d\theta }{dx}$

1. for x=5, 10, 15 and 20.

Interpret the result in b..

Evaluate $\frac{d\theta }{dx}$ for x = 25, 30, 35 and 40

Interpret the result in d. At what distance x should the person stand to maximize his or her viewing angle?