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Which of the following statements is TRUE about a smooth function fat (a, b), if f(a, b) = c, fxx (a, b) = 2 fyy (a, b) - 3? 9 = c is relative minimum value of f. (a, b, c) is a saddle point. None of the given choices c is relative maximum value of f. No conclusion can be made about the point (a, b, c).

Which of the following statements is TRUE about a smooth function fat (a, b), if f(a, b) = c, fxx (a, b) = 2 fyy (a, b) - 3? 9 = c is relative minimum value of f. (a, b, c) is a saddle point. None of the given choices c is relative maximum value of f. No conclusion can be made about the point (a, b, c).

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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Which of the following statements is TRUE about a smooth function fat (a, b), if f(a, b) = c, fxx (a, b) = 2 · fyy (a, b) — 3? 9 = c is relative minimum value of f. (a, b, c) is a saddle point. None of the given choices c is relative maximum value of f. No conclusion can be made about the point (a, b, c).
Transcribed Image Text:Which of the following statements is TRUE about a smooth function fat (a, b), if f(a, b) = c, fxx (a, b) = 2 · fyy (a, b) — 3? 9 = c is relative minimum value of f. (a, b, c) is a saddle point. None of the given choices c is relative maximum value of f. No conclusion can be made about the point (a, b, c).
Which of the following values is the directional derivative of f(x, y) = = xe²y at the point (2, 0) in the direction of u = (1, √√3)? 4√3 4 1/2 + 1/√3 7 7 None of the given choices 1+4√3 1 2 +2√3
Transcribed Image Text:Which of the following values is the directional derivative of f(x, y) = = xe²y at the point (2, 0) in the direction of u = (1, √√3)? 4√3 4 1/2 + 1/√3 7 7 None of the given choices 1+4√3 1 2 +2√3
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