Let F(x, Y) = $x ^ { 4 }$ - $y ^ { 2 }$

question 11

Multiple Choice

Let f(x, y) = $x ^ { 4 }$ - $y ^ { 2 }$ + $3 x ^ { 2 }$ + 2y - 7. The first partial derivatives of f(x, y) are zero at the points $( 0,1 )$ and $( - 1,1 )$ Use the second derivative test to determine the nature of f(x, y) at each of these points.

• A) (0,1) neither relative maximum nor minimum, (-1, 1) maximum
• B) (0, 1) relative maximum, (-1, 1) relative minimum
• C) (0, 1) no conclusion possible, (-1, 1) minimum
• D) (-1, 1) relative maximum, (0, 1) neither relative maximum nor minimum
• E) none of these

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Definitions:

Cultural Influence

The impact that culture has on the way individuals perceive, behave, and interact within society, shaping their values, norms, and practices.

Executive Functions

Executive functions are a set of cognitive processes including attentional control, inhibitory control, working memory, and cognitive flexibility, which are necessary for the cognitive control of behavior.

Cognitive Processes

The mental actions or mechanisms by which knowledge is acquired, processed, and utilized, including perception, memory, and reasoning.

Intentionally Controlling

Deliberately exerting influence or authority over a person, situation, or environment to achieve a desired outcome.