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Let f a function that allows second derivatives: Vf(x, y) = (a²x-a²x², y² + ay) With a <0, it can be stated certainly that: A) The point (1,0,f(1,0)) is a saddle point of f and f reaches a maximum relative in the point (0,0). B) The point (0,0,f(0,0)) is a saddle point of f and f reaches a minimum relative in the point (0,- a). C) f reaches a maximum relative at point (1,0) and f reaches a minimum relative at point (0,0). D) The point (0,a, f(0,a)) is a saddle point of f and f reaches a maximum relative in the point (1,0).

Let f a function that allows second derivatives: Vf(x, y) = (a²x-a²x², y² + ay) With a <0, it can be stated certainly that: A) The point (1,0,f(1,0)) is a saddle point of f and f reaches a maximum relative in the point (0,0). B) The point (0,0,f(0,0)) is a saddle point of f and f reaches a minimum relative in the point (0,- a). C) f reaches a maximum relative at point (1,0) and f reaches a minimum relative at point (0,0). D) The point (0,a, f(0,a)) is a saddle point of f and f reaches a maximum relative in the point (1,0).

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 a function that allows second derivatives: Vf(x,y) = (a²x - a²x², y² + ay) With a <0, it can be stated certainly that: A) The point (1,0,f(1,0)) is a saddle point of f and f reaches a maximum relative in the point (0,0). B) The point (0,0,f(0,0)) is a saddle point of f and f reaches a minimum relative in the point (0,- a). C) f reaches a maximum relative at point (1,0) and f reaches a minimum relative at point (0,0). D) The point (0,a, f(0,a)) is a saddle point of f and f reaches a maximum relative in the point (1,0).
Transcribed Image Text:Let f a function that allows second derivatives: Vf(x,y) = (a²x - a²x², y² + ay) With a <0, it can be stated certainly that: A) The point (1,0,f(1,0)) is a saddle point of f and f reaches a maximum relative in the point (0,0). B) The point (0,0,f(0,0)) is a saddle point of f and f reaches a minimum relative in the point (0,- a). C) f reaches a maximum relative at point (1,0) and f reaches a minimum relative at point (0,0). D) The point (0,a, f(0,a)) is a saddle point of f and f reaches a maximum relative in the point (1,0).
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