Solve the Problem $f ( x , y , z ) = \frac { x } { y } + \frac { y } { z } + \frac { z } { x }$

question 79

Multiple Choice

Solve the problem.
-Find the derivative of the function $f ( x , y , z ) = \frac { x } { y } + \frac { y } { z } + \frac { z } { x }$ at the point $( - 7,7 , - 7 )$ in the direction in which the function increases most rapidly.

• A) \(\frac { 2 } { 7 } \sqrt { 2 }\)
• B) \(\frac { 2 } { 7 } \sqrt { 3 }\)
• C) \(\frac { 3 } { 7 } \sqrt { 2 }\)
• D) \(\frac { 3 } { 7 } \sqrt { 3 }\)

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Definitions:

Active Repressor Protein

A protein that binds to specific DNA sequences to inhibit the transcription of certain genes, controlling gene expression.

Inactive RNA Polymerase

An RNA polymerase enzyme in a resting state that is not involved in the transcription of DNA into RNA.

Negative Control

An experiment or part of an experiment where no response is expected, serving to highlight the effect of the experimental treatment.

Repressible Genes

Genes whose expression can be decreased or turned off by the presence of a specific molecule.