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Let f(x, y) = x³ - 3x + 3xy². (a) Verify that the following are critical points of f: (0, 1), (0, -1), (1,0), and (-1,0). (b) Classify each critical point as a local maximum, local minimum or saddle point.

Let f(x, y) = x³ - 3x + 3xy². (a) Verify that the following are critical points of f: (0, 1), (0, -1), (1,0), and (-1,0). (b) Classify each critical point as a local maximum, local 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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7. Let f(x, y) = x³ - 3x + 3xy². (a) Verify that the following are critical points of f: (0, 1), (0, -1), (1,0), and (-1,0). (b) Classify each critical point as a local maximum, local minimum or saddle point.
Transcribed Image Text:7. Let f(x, y) = x³ - 3x + 3xy². (a) Verify that the following are critical points of f: (0, 1), (0, -1), (1,0), and (-1,0). (b) Classify each critical point as a local maximum, local minimum or saddle point.
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