Kindly answer item #1 (B) Let f be a function of x and y with fx (xo, Yo) = 0 and fy (xo, Yo) = 0 for some (xo, Yo) €dom f. Suppose that the second-order partial derivatives of f are continuous on a disk centered at(x, yo). LetD(xo. Yo) = fxx (xo. Yo) fyy(xo, Yo) - [fxy (xo, Yo)]².1. If D(a, b) > 0 and fxx(a, b) > 0 then (a, b) is a local minimum of f.2. If D (a, b) > 0 and fxx(a, b) < 0 then (a, b) is a local maximum of f.3. If D (a, b) < 0 then (a, b) is a saddle point of f.4. If D (a, b) = 0 then the point (a, b) could be any of a minimum, maximum, or saddle point(the test is inconclusive) [1].The goal of this study is to show alternative condition/s when the second partial derivative testasserts D(a, b) = 0 or an inconclusive result. This will lead to a result of either a local minimumof for local maximum of for saddle point of f.

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(B) Let f be a function of x and y with fx (xo, Yo)= 0 and fy(xo, Yo) = 0 for some (xo, Yo) € dom f. Suppose that the second-order partial derivatives of f are continuous on a disk centered at (xo, Yo). Let D(xo. Yo) =fxx (xo. Yo) fyy (xo. Yo) - [fxy(xo. Yo)]². 1. If D (a, b)> 0 and fxx(a, b)> 0 then (a, b) is a local minimum of f.

(B) Let f be a function of x and y with fx (xo, Yo)= 0 and fy(xo, Yo) = 0 for some (xo, Yo) € dom f. Suppose that the second-order partial derivatives of f are continuous on a disk centered at (xo, Yo). Let D(xo. Yo) =fxx (xo. Yo) fyy (xo. Yo) - [fxy(xo. Yo)]². 1. If D (a, b)> 0 and fxx(a, b)> 0 then (a, b) is a local minimum of f.

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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