Consider the function ƒ(x, y) = x2 + y2 + 2xy - x - y + 1 over the square 0 <=x <= 1 and 0<= y <=1. a. Show that ƒ has an absolute minimum along the line segment 2x + 2y = 1 in this square. What is the absolute minimum value? b. Find the absolute maximum value of ƒ over the square.
Consider the function ƒ(x, y) = x2 + y2 + 2xy - x - y + 1 over the square 0 <=x <= 1 and 0<= y <=1. a. Show that ƒ has an absolute minimum along the line segment 2x + 2y = 1 in this square. What is the absolute minimum value? b. Find the absolute maximum value of ƒ over the square.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Consider the function ƒ(x, y) = x2 + y2 + 2xy - x - y + 1 over the square 0 <=x <= 1 and 0<= y <=1.
a. Show that ƒ has an absolute minimum along the line segment 2x + 2y = 1 in this square. What is the absolute minimum value?
b. Find the absolute maximum value of ƒ over the square.
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