Find the Derivative of the Function at P0 in the Direction

question 135

Multiple Choice

Find the derivative of the function at P0 in the direction of u.
- $f ( x , y , z ) = 2 x y ^ { 3 } z ^ { 2 } , \quad P _ { 0 } ( 2,8,4 ) , \quad \mathbf { u } = - 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$

• A) \(- 16,384\)
• B) \(- \frac { 57,344 } { 3 }\)
• C) \(- \frac { 53,248 } { 3 }\)
• D) \(- 20,480\)

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Definitions:

Interaction Effects

Occur when the effect of one independent variable on a dependent variable changes depending on the level of another independent variable.

Main Effects

The direct, independent impacts of individual independent variables on a dependent variable in the context of factorial designs.

Total Mean

The overall average of a set of numbers or measurements, calculated by summing all the values and dividing by the number of observations.

Total Mean

The overall average of a set of numerical values computed by summing them up and dividing by the count of numbers.