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)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

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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