Consider the function f(x, y) = 2x² - 4x − xy² + 2y² − 3. - - (a) Find the first-order and second-order partial derivatives of f(x,y). Use the chain rule for small changes to estimate the change in f that occurs when (x, y) changes from (0, 1) to (0.01, 0.99). (b) (c) Show that the stationary points of f(x, y) are at (2,-2), (1,0) and (2, 2). (d) Use the eigenvalue test to classify each of the stationary points.
Consider the function f(x, y) = 2x² - 4x − xy² + 2y² − 3. - - (a) Find the first-order and second-order partial derivatives of f(x,y). Use the chain rule for small changes to estimate the change in f that occurs when (x, y) changes from (0, 1) to (0.01, 0.99). (b) (c) Show that the stationary points of f(x, y) are at (2,-2), (1,0) and (2, 2). (d) Use the eigenvalue test to classify each of the stationary points.
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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(c) and (d) please
Transcribed Image Text:Consider the function
f(x, y) = 2x² - 4x − xy² + 2y² − 3.
-
-
(a) Find the first-order and second-order partial derivatives of f(x,y).
Use the chain rule for small changes to estimate the change in f that
occurs when (x, y) changes from (0, 1) to (0.01, 0.99).
(b)
(c)
Show that the stationary points of f(x, y) are at (2,-2), (1,0) and
(2, 2).
(d) Use the eigenvalue test to classify each of the stationary points.
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