Question: Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = 5x 2 - 3xy + x/z.

Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = 5x² - 3xy + x/z.
(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?

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