Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If fx(xo, Yo) = f(xo, Yo) = 0, then f has a relative extremum at ( (xo, Yo, ²o). True. False. f(x, y) = x² - y² then fx(0, 0) = f(0, 0) = 0, but (0, 0, 0) is a saddle point. False. f(x, y) = 1 - x² - y²has a relative maximum at (0, 0, 0). False. f(x, y, z) = x² + y² + z²has a relative minimum at (0, 0, 0).
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If fx(xo, Yo) = f(xo, Yo) = 0, then f has a relative extremum at ( (xo, Yo, ²o). True. False. f(x, y) = x² - y² then fx(0, 0) = f(0, 0) = 0, but (0, 0, 0) is a saddle point. False. f(x, y) = 1 - x² - y²has a relative maximum at (0, 0, 0). False. f(x, y, z) = x² + y² + z²has a relative minimum at (0, 0, 0).
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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Transcribed Image Text:Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If fx(xo, Yo) = f(xo, Yo) = 0, then f has a relative extremum at (
(xo, Yo, ²o).
True.
False. f(x, y) = x² - y² then fx(0, 0) = f(0, 0) = 0, but (0, 0, 0) is a saddle point.
False. f(x, y) = 1 - x² - y²has a relative maximum at (0, 0, 0).
False. f(x, y, z) = x² + y² + z²has a relative minimum at (0, 0, 0).
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