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Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax? + a?x, y? - ay) with a > 0. It can be stated with certainty that: A) The point (-a, a, f(-a, a)) is a saddle point of f and f attains a relative maximum at the point. (0, a). B) The point (0, 0, f(0, 0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, a). C) The point (0, 0, f(0, 0)) is a saddle point of f and f reaches a relative minimum at the point (-a, 0). D) f attains a relative maximum at the point (-a, a) and f attains a relative minimum at the point (-a, 0)

Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax? + a?x, y? - ay) with a > 0. It can be stated with certainty that: A) The point (-a, a, f(-a, a)) is a saddle point of f and f attains a relative maximum at the point. (0, a). B) The point (0, 0, f(0, 0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, a). C) The point (0, 0, f(0, 0)) is a saddle point of f and f reaches a relative minimum at the point (-a, 0). D) f attains a relative maximum at the point (-a, a) and f attains a relative minimum at the point (-a, 0)

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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Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax?+ a?x, y? - ay) with a > 0. It can be stated with certainty that: A) The point (-a, a, f(-a, a)) is a saddle point of f and f attains a relative maximum at the point. (0, a). B) The point (0, 0, f(0, 0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, a). C) The point (0, 0, f(0, 0)) is a saddle point of f and f reaches a relative minimum at the point (-a, 0). D) f attains a relative maximum at the point (-a, a) and f attains a relative minimum at the point (-a, 0)
Transcribed Image Text:Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax?+ a?x, y? - ay) with a > 0. It can be stated with certainty that: A) The point (-a, a, f(-a, a)) is a saddle point of f and f attains a relative maximum at the point. (0, a). B) The point (0, 0, f(0, 0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, a). C) The point (0, 0, f(0, 0)) is a saddle point of f and f reaches a relative minimum at the point (-a, 0). D) f attains a relative maximum at the point (-a, a) and f attains a relative minimum at the point (-a, 0)
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