Solve the Problem $- \frac { 5 } { 34 } \sqrt { 2 }$

question 94

Multiple Choice

Solve the problem.
-Find the derivative of the function f(x, y, z) = ln(xy + yz + zx) at the point (-2, -4, -6) in the direction in which the function decreases most rapidly.

• A) \(- \frac { 5 } { 34 } \sqrt { 2 }\)
• B) \(- \frac { 5 } { 26 } \sqrt { 2 }\)
• C) \(- \frac { 5 } { 14 } \sqrt { 2 }\)
• D) \(- \frac { 5 } { 22 } \sqrt { 2 }\)

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Definitions:

Geometric Tolerances

The limits of allowable variation in the shape and size of a part's geometry, including its form, orientation, and location, specified in engineering drawings.

Straightness

A condition where an element or line maintains a consistent path without deviation, typically applied in manufacturing to ensure parts are within specified tolerances.

Flatness

A geometric tolerance that describes how flat a surface must be within specified limits.

Tertiary Plane

A plane that is oriented to intersect or be parallel with the primary and secondary planes in a three-dimensional coordinate system.