Suppose that in a certain region of space the electric potential V is given by the function V (x, y, z) = 5x2 −3xy + xyz a) Determine the rate of change of the potential at P = (3,4,5) in the direction of the vector v = (1, −1, 1). b) In what direction does V change faster in P? c) What is the maximum rate of change of V in P?

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