A farmer wishes to enclose a region of land in the first quadrant of the Cartesian plane under the graph of the function f(x)= x=1, x E (0, 0). The region in question is to be of the form A = {(x, y) E R² : s
A farmer wishes to enclose a region of land in the first quadrant of the Cartesian plane under the graph of the function f(x)= x=1, x E (0, 0). The region in question is to be of the form A = {(x, y) E R² : s
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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Transcribed Image Text:A farmer wishes to enclose a region of land in the first quadrant of the Cartesian plane under the graph
of the function f(x) = x=1, x E (0, 0). The region in question is to be of the form
= {(x, y) E R² : s < x<t and 0 < y < f(x)}
A =
where s and t are parameters that determine the shape of the region, and 0 < s < t. The region is to be
fenced on all four sides. Three of these sides are straight line segments to be made out of fence that must
be bought at R200 per unit distance: these three sides are the West side, the South side and the East side
(assume that the y-axis points North and the x-axis points East). The North side of the region is part
of the graph of f and is to be made out of very cheep fencing that the farmer already has, and this will
not cost any money. We are dealing with the problem from a purely two dimensional perspective, and the
height of the fence is not part of the problem. The farmer already has all remaining materials that are
needed besides the fence (i.e. corner poles, equipment etc.). The region is to have a total area of 1, and the
farmer wishes to minimize the cost of the fencing that must be bought.
Draw a two dimensional diagram of the region in the Cartesian plane and find the minimum possible
cost to fence such a region as described above.
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