Given the quadratic function f(x, y) = x² + 2y²-ry-5x+13y - 22 (1) Put it in quadratic form to find the position of the vertex (all 3 coordinates) Quadratic form: Coordinates of the vertex (2) Compute of/or and af/dy. af/ar= af/dy=. (1) (3) Verify that both partial derivatives are 0 at the vertex of the function. Briefly explain why this may be the case. (4) Is the graph of this function a paraboloid or a saddle? (Justify your answer; guesses will not count).

Given the quadratic function f(x, y) = x² + 2y²-ry-5x+13y - 22 (1) Put it in quadratic form to find the position of the vertex (all 3 coordinates) Quadratic form: Coordinates of the vertex (2) Compute of/or and af/dy. af/ar= af/dy=. (1) (3) Verify that both partial derivatives are 0 at the vertex of the function. Briefly explain why this may be the case. (4) Is the graph of this function a paraboloid or a saddle? (Justify your answer; guesses will not count).

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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Question

Heading "Quadratic functions" Please mention number of all required parts Needed to be solved correctly by showing Each parts numbering By hand solution needed

2 Quadratic functions
Given the quadratic function
f(x, y) = x² + 2y²2 - xy -5x + 13y - 22
(1) Put it in quadratic form to find the position of the vertex (all 3 coordinates)
Quadratic form:
Coordinates of the vertex
(2) Compute of/or and af/ay.
əflər
Әf/ду
(1)
(3) Verify that both partial derivatives are 0 at the vertex of the function. Briefly explain why this
may be the case.
(4) Is the graph of this function a paraboloid or a saddle ? (Justify your answer; guesses will not count).

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