A photographer takes a picture of a three-foot-tall painting hanging in an art gallery. The camera lens is 1 foot below the lower edge of the painting (see figure). The angle β subtended by the camera lens x feet from the painting is given by β = arctan 3x / x2 + 4, x > 0.

(a) Use a graphing utility to graph β as a function of x.
(b) Use the graph to approximate the distance from the picture when β is maximum.
(c) Identify the asymptote of the graph and interpret its meaning in the context of the problem.

Transcribed Image Text:

3 ft Not drawn to scale