f(x, y) = x² + 2y²-ay-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 8f/0x and Of/8y. of/0x Of/dy (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).
f(x, y) = x² + 2y²-ay-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 8f/0x and Of/8y. of/0x Of/dy (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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Heading Q2 or Quadratic functions
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Transcribed Image Text:2 Quadratic functions
Given the quadratic function
f(x, y) = x² + 2y² - 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/0x and af/ay.
af/0x=
Әf/ду
(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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