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Let f a function that allows continuous second partial derivatives: Vf(x, y) = (x³ - ax², y² - ay) With a < 0, it can be stated certainly that: A) The point (0,a, f(0,a)) is a saddle point of f and f reaches a minimum relative in the point (a,a). B) The point (a,a, f(a,a)) is a saddle point of f and f reaches a minimum relative in the point (0,0). C) The point (-a,a, f(-a,a)) is a saddle point of f and f reaches a minimum relative in the point (a,0). D) The point (a,0, f(a,0)) is a saddle point of f and f reaches a maximum relative at point (0,a).

Let f a function that allows continuous second partial derivatives: Vf(x, y) = (x³ - ax², y² - ay) With a < 0, it can be stated certainly that: A) The point (0,a, f(0,a)) is a saddle point of f and f reaches a minimum relative in the point (a,a). B) The point (a,a, f(a,a)) is a saddle point of f and f reaches a minimum relative in the point (0,0). C) The point (-a,a, f(-a,a)) is a saddle point of f and f reaches a minimum relative in the point (a,0). D) The point (a,0, f(a,0)) is a saddle point of f and f reaches a maximum relative at point (0,a).

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 continuous second partial derivatives: Vf(x,y) = (x³ ax²,y² - ay) With a < 0, it can be stated certainly that: A) The point (0,a, f(0,a)) is a saddle point of f and f reaches a minimum relative in the point (a,a). B) The point (a,a, f(a,a)) is a saddle point of f and f reaches a minimum relative in the point (0,0). C) The point (-a,a, f(-a,a)) is a saddle point of f and f reaches a minimum relative in the point (a,0). D) The point (a,0, f(a,0)) is a saddle point of f and f reaches a maximum relative at point (0,a). H = (fxx · fyy ) - fxy
Transcribed Image Text:Let f a function that allows continuous second partial derivatives: Vf(x,y) = (x³ ax²,y² - ay) With a < 0, it can be stated certainly that: A) The point (0,a, f(0,a)) is a saddle point of f and f reaches a minimum relative in the point (a,a). B) The point (a,a, f(a,a)) is a saddle point of f and f reaches a minimum relative in the point (0,0). C) The point (-a,a, f(-a,a)) is a saddle point of f and f reaches a minimum relative in the point (a,0). D) The point (a,0, f(a,0)) is a saddle point of f and f reaches a maximum relative at point (0,a). H = (fxx · fyy ) - fxy
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