A rectangular billboard 9 feet in height stands in a field so that its bottom is 6 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard. Express 0, the vertical angle subtended by the billboard at her eye, in terms of x. Then find the distance xo the cow must stand from the billboard to maximize 0.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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The Nearsighted Cow Problem: A Calculus Classic.
A rectangular billboard 9 feet in height stands in a field
so that its bottom is 6 feet above the ground. A
nearsighted cow with eye level at 4 feet above the
ground stands x feet from the billboard. Express 0, the
vertical angle subtended by the billboard at her eye, in
terms of x. Then find the distance xo the cow must
stand from the billboard to maximize 0.
0(x) =
O is maximized when xo =
Nearsighted Cow Problem
( Click on image for a larger view)
Transcribed Image Text:The Nearsighted Cow Problem: A Calculus Classic. A rectangular billboard 9 feet in height stands in a field so that its bottom is 6 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard. Express 0, the vertical angle subtended by the billboard at her eye, in terms of x. Then find the distance xo the cow must stand from the billboard to maximize 0. 0(x) = O is maximized when xo = Nearsighted Cow Problem ( Click on image for a larger view)
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