Problem: A painting is hung so that the top isbfeet above your eye level while the bottom isafeet above your eye level. Letxbe the distance between you and the wall that holds the painting. Your goal is to stand in a place such that the angle θ subtended by the painting at your eye (i.e. the angle between the top and the bottom of the painting with respect to your eye) is as large as possible.

1. Express θ as a function of x.

2. Determine the values of x for which θ is increasing and the values of x for which θ is decreasing.

3. Use your answer to the above to determine where you should stand.

Solution:

θ = arctan(b/x) - arctan(a/x)

θ' = [-a/(x^{2}(1+a^{2}/x^{2}))] + [b/(x^{2}(1+b^{2}/x^{2}))]

Then I'm stuck on number 2 and 3?