Determine the Nature of the Critical Points of the Function $f ( x , y ) = 3 x ^ { 5 } y + x y ^ { 5 } + x y$

question 54

Multiple Choice

Determine the nature of the critical points of the function $f ( x , y ) = 3 x ^ { 5 } y + x y ^ { 5 } + x y$

• A)f has a saddle point at (1, 0).
• B)f has a local maximum at (0, 0).
• C)f has a saddle point at (0, 1).
• D)f has a saddle point at (0, 0).
• E)f has a local minimum at (0, 0).

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Definitions:

Physical Distance

The measure of space between two objects or places, often affecting social interactions and perceptions.

Mindlessness

A mental state characterized by a lack of conscious awareness or reflexive use of memorized behavior and thought patterns, often leading to errors or oversight in tasks.

Compliance

The act of conforming to or following rules, standards, or laws, or yielding to a request or desire from others.

Obedience

Following orders or directives from an authority figure without questioning.