Suppose That Over a Certain Region of Space the Electrical $V$

Multiple Choice

Suppose that over a certain region of space the electrical potential $V$ is given by $V ( x , y , z ) = 8 x ^ { 2 } - 7 x y + 7 x y z$ .
Find the rate of change of the potential at $( - 1,1 , - 1 )$ in the direction of the vector $\mathbf { v } = 7 \mathbf { i } + 10 \mathbf { j } - 8 \mathbf { k }$ .

A) $- 15.099$
B) $14.569856$
C) 44
D) 20
E) $- 0.96$