Suppose That $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$

question 65

Multiple Choice

Suppose that $f ( x , y ) = x ^ { 2 } + 3 x y + y ^ { 2 }$ Find a normal vector to the tangent plane of f at the point (1, 1) .Select all that apply.

• A) \(5 \vec { i } + 5 \vec { j } - \vec { k }\)
• B) \(5 \vec { i } + 5 \vec { j } + \vec { k }\)
• C) \(- 5 \vec { i } - 5 \vec { j } + \vec { k }\)
• D) \(- 5 \vec { i } + 5 \vec { j } + \vec { k }\)

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Definitions:

Aging

The process of becoming older, which includes biological, emotional, intellectual, and social changes.

Hypothalamus

A region of the brain that regulates basic biological needs and motivational systems such as hunger, thirst, and body temperature.

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A natural condition that impacts both mind and body, marked by a change in consciousness, reduced sensory experiences, and a suppression of most voluntary muscle movements.

Suprachiasmatic Nucleus

A region in the brain located in the hypothalamus, responsible for regulating circadian rhythms through its control over sleep-wake cycles.