Find the Directional Derivative of the Function at P in the Direction

question 91

Multiple Choice

Find the directional derivative of the function at P in the direction of $\overrightarrow { \mathbf { v } } \text {. }$ $f ( x , y , z ) = x y + y z + x z , P ( 1,1,1 ) , \quad \overrightarrow { \mathbf { v } } = 4 \hat { \mathbf { i } } + 5 \hat { \mathbf { j } } - 3 \hat { \mathbf { k } }$

• A) \(4 / 5 \sqrt { 2 }\)
• B) \(- 8 / 5 \sqrt { 2 }\)
• C) \(12 / 5 \sqrt { 2 }\)
• D) \(24 / 5 \sqrt { 2 }\)
• E) \(- 24 / 5 \sqrt { 2 }\)

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Definitions:

Euphoria

A feeling or state of intense excitement and happiness.

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Thoughts that are excessively concerned with death, disease, or other distressing themes, often seen in various mental health conditions.

Bulimia Nervosa

An eating disorder characterized by episodes of binge eating followed by compensatory behaviors, such as vomiting, to prevent weight gain.

Binge-And-Purge

A cycling behavior often associated with bulimia nervosa, involving episodes of excessive eating followed by attempts to avoid weight gain through vomiting, using laxatives, or exercising excessively.