Find the Linearization of the Function at the Given Point $f ( x , y , z ) = \tan ^ { - 1 } x y z$

question 13

Multiple Choice

Find the linearization of the function at the given point.
- $f ( x , y , z ) = \tan ^ { - 1 } x y z$ at $( 9,9,9 )$

• A) \(L ( x , y , z ) = \frac { 81 } { 6562 } x + \frac { 81 } { 6562 } y + \frac { 81 } { 6562 } z + \tan ^ { - 1 } 81 - \frac { 243 } { 6562 }\)
• B) \(L ( x , y , z ) = \frac { 81 } { 6562 } x + \frac { 81 } { 6562 } y + \frac { 81 } { 6562 } z + \tan ^ { - 1 } 729 - \frac { 243 } { 6562 }\)
• C) \(L ( x , y , z ) = \frac { 81 } { 531,442 } x + \frac { 81 } { 531,442 } y + \frac { 81 } { 531,442 } z + \tan ^ { - 1 } 729 - \frac { 2187 } { 531,442 }\)
• D) \(\mathrm { L } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \frac { 81 } { 531,442 } \mathrm { x } + \frac { 81 } { 531,442 } \mathrm { y } + \frac { 81 } { 531,442 } \mathrm { z } + \tan ^ { - 1 } 81 - \frac { 2187 } { 531,442 }\)

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