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Consider the function f(x,y) = 2x2 - 4x – xy² + 2y² = 3. %3D (a) Find the first-order and second-order partial derivatives of f(x, y). (b) 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). (c) Show that the stationary points of f(x, y) are at (2,-2), (1,0) and (2, 2).

Consider the function f(x,y) = 2x2 - 4x – xy² + 2y² = 3. %3D (a) Find the first-order and second-order partial derivatives of f(x, y). (b) 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). (c) Show that the stationary points of f(x, y) are at (2,-2), (1,0) and (2, 2).

Advanced Engineering Mathematics
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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Q1 a,b,c
Consider the function f(x,y) = 2x2 - 4x - ry + 2y² 3. (a) Find the first-order and second-order partial derivatives of f(x, y). (b) 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). (c) Show that the stationary points of f(x, y) are at (2,-2), (1,0) and (2, 2).
Transcribed Image Text:Consider the function f(x,y) = 2x2 - 4x - ry + 2y² 3. (a) Find the first-order and second-order partial derivatives of f(x, y). (b) 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). (c) Show that the stationary points of f(x, y) are at (2,-2), (1,0) and (2, 2).
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