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

question 381

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 decreases most rapidly.

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

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