' Let f: R? →R be defined by S(2) = (r - r2)* +2} +3– 2r + 2r2 where a = [71, r2]". Suppose that we wish to minimize f over R². (a) |Write the function f in terms of the following quadratic form S(2) = z'Qz +b'z where Q is symmetric. (b) i Find all points satisfying the First Order Necessary Condition. Do these points satisfy the Second Order Sufficient Condition? Find all local minimum point(s). Are they also global minimum point(s)?

' Let f: R? →R be defined by S(2) = (r - r2)* +2} +3– 2r + 2r2 where a = [71, r2]". Suppose that we wish to minimize f over R². (a) |Write the function f in terms of the following quadratic form S(2) = z'Qz +b'z where Q is symmetric. (b) i Find all points satisfying the First Order Necessary Condition. Do these points satisfy the Second Order Sufficient Condition? Find all local minimum point(s). Are they also global minimum point(s)?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 29E

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