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A. Let S, be the set of points in the (x₁, x₂) plane that minimizes the function f(x₁, x₂) = (4x₁ + 3x₂10)2. Describe Sy using set notation, and draw a graph in the (x₁, x₂) plane that shows the set Sf (Hint: the set is a line). B. From (A) we know there is more than one pair (x₁, x₂) that minimizes f(x₁,x₂). Find the point (x₁, x₂) in Sf that minimizes the length of the vector (x₁, x₂) (note the length of the vector is the distance between (0,0) and the point (x₁, x₂).

A. Let S, be the set of points in the (x₁, x₂) plane that minimizes the function f(x₁, x₂) = (4x₁ + 3x₂10)2. Describe Sy using set notation, and draw a graph in the (x₁, x₂) plane that shows the set Sf (Hint: the set is a line). B. From (A) we know there is more than one pair (x₁, x₂) that minimizes f(x₁,x₂). Find the point (x₁, x₂) in Sf that minimizes the length of the vector (x₁, x₂) (note the length of the vector is the distance between (0,0) and the point (x₁, x₂).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Comparing L2 and L1 A. Let S, be the set of points in the (x₁, x₂) plane that minimizes the function f(x₁, x₂) = (4x₁ + 3x₂10)². Describe Sy using set notation, and draw a graph in the (x₁, x₂) plane that shows the set S, (Hint: the set is a line). B. From (A) we know there is more than one pair (x₁, x₂) that minimizes f(x₁,x₂). Find the point (x₁, x₂) in Sf that minimizes the length of the vector (x₁, x₂) (note the length of the vector is the distance between (0,0) and the point (x₁, x₂).
Transcribed Image Text:1. Comparing L2 and L1 A. Let S, be the set of points in the (x₁, x₂) plane that minimizes the function f(x₁, x₂) = (4x₁ + 3x₂10)². Describe Sy using set notation, and draw a graph in the (x₁, x₂) plane that shows the set S, (Hint: the set is a line). B. From (A) we know there is more than one pair (x₁, x₂) that minimizes f(x₁,x₂). Find the point (x₁, x₂) in Sf that minimizes the length of the vector (x₁, x₂) (note the length of the vector is the distance between (0,0) and the point (x₁, x₂).
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