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When using the method of Lagrange multipliers to find the extrema of the function f = x² + 3y subject to the constraint g = x + y − 1 = 0, one has to solve a system of three equations for the three variables x, y, A. The solution of this system is a set of eight points (x, y, X), which can be regarded as points in three- space. Let A be the sum of the distances of those points (x, y, A) to the origin (0, 0, 0). Let m be the minimum of f and let M be the maximum. Then cos(3A/4) + sin(m) + sin(M) is O -1.967 O 0.200 O-2.175 O 0.502 O -0.064 O 0.519 O 1.995 O -2.752

When using the method of Lagrange multipliers to find the extrema of the function f = x² + 3y subject to the constraint g = x + y − 1 = 0, one has to solve a system of three equations for the three variables x, y, A. The solution of this system is a set of eight points (x, y, X), which can be regarded as points in three- space. Let A be the sum of the distances of those points (x, y, A) to the origin (0, 0, 0). Let m be the minimum of f and let M be the maximum. Then cos(3A/4) + sin(m) + sin(M) is O -1.967 O 0.200 O-2.175 O 0.502 O -0.064 O 0.519 O 1.995 O -2.752

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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When using the method of Lagrange multipliers to find the extrema of the function f = x² + 3y subject to the constraint g = x + y − 1 = 0, one has to solve a system of three equations for the three variables x, y, A. The solution of this system is a set of eight points (x, y, X), which can be regarded as points in three- space. Let A be the sum of the distances of those points (x, y, A) to the origin (0, 0, 0). Let m be the minimum of f and let M be the maximum. Then cos(3A/4) + sin(m) + sin(M) is O -1.967 O 0.200 O-2.175 O 0.502 O -0.064 O 0.519 O 1.995 O -2.752
Transcribed Image Text:When using the method of Lagrange multipliers to find the extrema of the function f = x² + 3y subject to the constraint g = x + y − 1 = 0, one has to solve a system of three equations for the three variables x, y, A. The solution of this system is a set of eight points (x, y, X), which can be regarded as points in three- space. Let A be the sum of the distances of those points (x, y, A) to the origin (0, 0, 0). Let m be the minimum of f and let M be the maximum. Then cos(3A/4) + sin(m) + sin(M) is O -1.967 O 0.200 O-2.175 O 0.502 O -0.064 O 0.519 O 1.995 O -2.752
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