Question 2 Given the function of two variables f(x, y) = -5x² - 2xy-8y²-8. a) [ Use Lagrange Multipliers to find the extreme value(s) of the function f subject to the constraint -4x + y - 4 = 0. 39

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 3E
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Question 2
Given the function of two variables
f(x, y) = -5x² - 2xy-8y2²-8.
a) [
1 Use Lagrange Multipliers to find the extreme value(s) of the function f subject
to the constraint -4x + y - 4 = 0.
b) Verify that f(x, y) = (5x + y)²-(y² + 8) and show that ƒ has
maximum and no minimum with the constraint -4x + y - 4 = 0.
Transcribed Image Text:Question 2 Given the function of two variables f(x, y) = -5x² - 2xy-8y2²-8. a) [ 1 Use Lagrange Multipliers to find the extreme value(s) of the function f subject to the constraint -4x + y - 4 = 0. b) Verify that f(x, y) = (5x + y)²-(y² + 8) and show that ƒ has maximum and no minimum with the constraint -4x + y - 4 = 0.
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