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Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax² – x, y? – a²) - | with a < 0. It is possible to assemble with certainty that a) The point (÷, a, f(÷, a)) is a saddle point of f and f reaches a relative maximum at the point (0, a). a (). b) The point a)) is a saddle point of f and f reaches a relative maximum at the point а). 1 c) The point (0, a, f(0, a)) is a saddle point of f and f reaches a relative minimum at the point (÷, a). d) The point (0,-a, f(0,-a)) is a saddle point of f and f reaches a relative minimum at the point (0, a).

Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (ax² – x, y? – a²) - | with a < 0. It is possible to assemble with certainty that a) The point (÷, a, f(÷, a)) is a saddle point of f and f reaches a relative maximum at the point (0, a). a (). b) The point a)) is a saddle point of f and f reaches a relative maximum at the point а). 1 c) The point (0, a, f(0, a)) is a saddle point of f and f reaches a relative minimum at the point (÷, a). d) The point (0,-a, f(0,-a)) is a saddle point of f and f reaches a relative minimum at the 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 be a function admitting continuous second partial derivatives such that Vf(x, y) = (a.x² – x, y? – a²) - | with a < 0. It is possible to assemble with certainty that 1 a) The point (÷, a, f(÷, a)) is a saddle point of f and f reaches a relative maximum at the point (0, a). a (-0). b) The point a)) is a saddle point of f and f reaches a relative maximum at the point а). 1 c) The point (0, a, f(0, a)) is a saddle point of f and f reaches a relative minimum at the point (÷, a). d) The point (0,-a, f(0,-a)) is a saddle point of f and f reaches a relative minimum at the point (0, a).
Transcribed Image Text:Let f be a function admitting continuous second partial derivatives such that Vf(x, y) = (a.x² – x, y? – a²) - | with a < 0. It is possible to assemble with certainty that 1 a) The point (÷, a, f(÷, a)) is a saddle point of f and f reaches a relative maximum at the point (0, a). a (-0). b) The point a)) is a saddle point of f and f reaches a relative maximum at the point а). 1 c) The point (0, a, f(0, a)) is a saddle point of f and f reaches a relative minimum at the point (÷, a). d) The point (0,-a, f(0,-a)) is a saddle point of f and f reaches a relative minimum at the point (0, a).
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