Calculus Homework Help

Question

A rectangular billboard 5 feet in height stands in a field so that its bottom is 10 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands  feet from the billboard. Express , the vertical angle subtended by the billboard at her eye, in terms of . Then find the distance  the cow must stand from the billboard to maximize.

Answer 1

tan T = 6/x

T = inverse_tangent(6/x)

dT/dx = 1/ (1 + (6/x)^2) = 1/(1 + (36/x^2)) = reciprocal [( x^2 + 36)/x^2] = x^2/(x^2 + 36)

max at x=0....

cow must stand directly in front of the billboard