Solve the Problem $f ( x , y , z ) = x y ^ { 3 } z ^ { 2 }$

Multiple Choice

Solve the problem.
-About how much will $f ( x , y , z ) = x y ^ { 3 } z ^ { 2 }$ change if the point $( x , y , z )$ moves from $( 3 , - 7 , - 6 )$ a distance of $\mathrm { ds } = \frac { 1 } { 10 }$ unit in the direction of $2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k }$ ?

A) $\frac { 2646 } { 5 }$
B) $\frac { 882 } { 5 }$
C) $- \frac { 2646 } { 5 }$
D) $- \frac { 882 } { 5 }$