3. Consider the function f defined by f(x, y) = 4x² + 4y² + x² + y² − 6x²y². af af (a) Find and dx ду (b) Find the five stationary points of f. a²ƒ a²f a² f (c) Calculate and " მ2 მომყ მყ2 * (d) Classify the stationary points as maxima, minima, or saddle points. Hint: By adding and subtracting the first order equations for the stationary points and taking out a common factor x+y and x - y respectively, the problem can be simplified. The classification of the four nontrivial points can be treated in one go.)
3. Consider the function f defined by f(x, y) = 4x² + 4y² + x² + y² − 6x²y². af af (a) Find and dx ду (b) Find the five stationary points of f. a²ƒ a²f a² f (c) Calculate and " მ2 მომყ მყ2 * (d) Classify the stationary points as maxima, minima, or saddle points. Hint: By adding and subtracting the first order equations for the stationary points and taking out a common factor x+y and x - y respectively, the problem can be simplified. The classification of the four nontrivial points can be treated in one go.)
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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Could you please do all parts and provide written solutions , with explanations
Transcribed Image Text:4
3. Consider the function f defined by ƒ(x, y) = 4x² + 4y² + x² + y² − 6x²y².
af
(a) Find and
af
əx ду
(b) Find the five stationary points of f.
a²ƒ 8² f
8² f
(c) Calculate
and
дх2’дхду
მყ2
(d) Classify the stationary points as maxima, minima, or saddle points.
Hint: By adding and subtracting the first order equations for the stationary points and taking out a
common factor x +y and x
y respectively, the problem can be simplified. The classification of the four
nontrivial points can be treated in one go.)
-
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