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10 (2). Let f be a function that admits continuous second partial derivatives such that Vf (x, y) = (a'x - a'x², y² + ay) with a <0. It can be stated with certainty that: A) f reaches a relative maximum at the point (1, 0) and f reaches a relative minimum at the point (0, 0 B) The point (0, 0, f (0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, -a). C) The point (0, a, f (0, a)) is a saddle point of f and f reaches a relative maximum at the point (1, 0). D) The point (1, 0, f (1, 0)) is a saddle point of f and f reaches a relative maximum at the point (0, 0).

10 (2). Let f be a function that admits continuous second partial derivatives such that Vf (x, y) = (a'x - a'x², y² + ay) with a <0. It can be stated with certainty that: A) f reaches a relative maximum at the point (1, 0) and f reaches a relative minimum at the point (0, 0 B) The point (0, 0, f (0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, -a). C) The point (0, a, f (0, a)) is a saddle point of f and f reaches a relative maximum at the point (1, 0). D) The point (1, 0, f (1, 0)) is a saddle point of f and f reaches a relative maximum at the point (0, 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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10 (2). Let f be a function that admits continuous second partial derivatives such that Vf (x, y) = (a'x - a'x?, y? + ay) with a <0. It can be stated with certainty that: A) f reaches a relative maximum at the point (1, 0) and f reaches a relative minimum at the point (0, 0). B) The point (0, 0, f (0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, -a). C) The point (0, a, f (0, a)) is a saddle point of f and f reaches a relative maximum at the point (1, 0). D) The point (1, 0, f (1, 0)) is a saddle point of f and f reaches a relative maximum at the point (0, 0).
Transcribed Image Text:10 (2). Let f be a function that admits continuous second partial derivatives such that Vf (x, y) = (a'x - a'x?, y? + ay) with a <0. It can be stated with certainty that: A) f reaches a relative maximum at the point (1, 0) and f reaches a relative minimum at the point (0, 0). B) The point (0, 0, f (0, 0)) is a saddle point of f and f reaches a relative minimum at the point (0, -a). C) The point (0, a, f (0, a)) is a saddle point of f and f reaches a relative maximum at the point (1, 0). D) The point (1, 0, f (1, 0)) is a saddle point of f and f reaches a relative maximum at the point (0, 0).
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