The Nearsighted Cow Problem: A Calculus Classic.

A rectangular billboard 6 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 [math] feet from the billboard. Express [math], the vertical angle subtended by the billboard at her eye, in terms of [math]. Then find the distance [math] the cow must stand from the billboard to maximize [math].

[math] = [math] is maximized when [math] =

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