Please review the following for accuracy and please provide corrections where necessary: Consider the function f(x, y) = 2x² − y² + 4x + 6y subject to x + 2y = 20 a) Find the extreme point b) Determine the nature of the extreme pointI found the first order conditions to be: Equation 1: 4x + 4 - λ = 0Equation 2: -2y +6 -2λ =0Equation 3: x+2y-20 =0 021 =4ax2321-2ay2²fст=dxdy dxdy= 0Then the matrix becomes:H01 = [1 −2]Det (HI) [4-200-2-2]wwwwww=(4-2)(-21)(4-2)(-2) = 0 and (4)(1 + 2) = 0The corresponding eigenvalues are:21=42.2=-2One negative and one positive eigenvalue denotes a saddle point. Therefore, it is found that the extreme point for (x,y) is (6,23)c) Determine the nature of the extreme point4To determine the nature of the extreme point, test the second order derivatives8x2dxdyH=дудх ду²Therefore, given L(x)= 2x² - y²+4x+6y-λ(x+2y-20)

Answered: Image /qna-images/answer/e05f2def-ae48-4d47-8a6e-f0cc2e6e15e5.jpg

Answered: Consider the function f(x, y) = 2x² −…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Question

Please review the following for accuracy and please provide corrections where necessary: Consider the function f(x, y) = 2x² − y² + 4x + 6y subject to x + 2y = 20 a) Find the extreme point b) Determine the nature of the extreme point I found the first order conditions to be: Equation 1: 4x + 4 - λ = 0 Equation 2: -2y +6 -2λ =0 Equation 3: x+2y-20 =0