Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, у, 2) %3D 5x2 - 3ху + хуz (a) Find the rate of change of the potential at P(4, 2, 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?

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