# Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = x^2 − 3xy + xyz. (a) Find the rate of change of the potential at P(3,4,5)

Question

Suppose that over a certain region of space the electrical
potential V is given by V(x, y, z) = x^2 − 3xy + xyz.
(a) Find the rate of change of the potential at P(3,4,5) in
the direction of the vector v= i − j+ k.
(b) In which direction does V change most rapidly at P?
(c) What is the maximum rate of change at P?