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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