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- (a) Let ƒ be defined for all (x, y) by ƒ(x, y) = x³ + y³ – 3xy. Show that (0,0) and (1,1) are the only stationary points, and compute the quadratic form for f at the stationary points. (b) Check the definiteness of the quadratic form at the stationary points. (c) Classify the stationary points (determine if they are a maximum, minimum, or saddle point).

- (a) Let ƒ be defined for all (x, y) by ƒ(x, y) = x³ + y³ – 3xy. Show that (0,0) and (1,1) are the only stationary points, and compute the quadratic form for f at the stationary points. (b) Check the definiteness of the quadratic form at the stationary points. (c) Classify the stationary points (determine if they are a maximum, minimum, or saddle point).

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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2. (a) Let f be defined for all (x, y) by f(x, y) = x³ + y³ − 3xy. Show that (0,0) and (1, 1) are the only stationary points, and compute the quadratic form for f at the stationary points. (b) Check the definiteness of the quadratic form at the stationary points. (c) Classify the stationary points (determine if they are a maximum, minimum, or saddle point).
Transcribed Image Text:2. (a) Let f be defined for all (x, y) by f(x, y) = x³ + y³ − 3xy. Show that (0,0) and (1, 1) are the only stationary points, and compute the quadratic form for f at the stationary points. (b) Check the definiteness of the quadratic form at the stationary points. (c) Classify the stationary points (determine if they are a maximum, minimum, or saddle point).
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