Provide an Appropriate Response $\mathrm { P } _ { 0 }$

Multiple Choice

Provide an appropriate response.
-Find the direction in which the function is increasing most rapidly at the point $\mathrm { P } _ { 0 }$ . $f ( x , y , z ) = x \sqrt { y ^ { 2 } + z ^ { 2 } } , P _ { 0 } ( 1,2,1 )$

A) $\sqrt { 30 } \left( \frac { \mathrm { i } } { 6 } + \frac { \mathrm { j } } { 15 } - \frac { \mathrm { k } } { 30 } \right)$
B) $\frac { 1 } { \sqrt { 30 } } \left( \frac { i } { 6 } + \frac { j } { 15 } - \frac { k } { 30 } \right)$
C) $\frac { 1 } { \sqrt { 30 } } \left( \frac { i } { 6 } + \frac { j } { 15 } + \frac { k } { 30 } \right)$
D) $\sqrt { 30 } \left( \frac { \mathrm { i } } { 6 } + \frac { \mathrm { j } } { 15 } + \frac { \mathrm { k } } { 30 } \right)$