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Suppose that over a certain region of space the electrical potential V is given by the...

Suppose that over a certain region of space the electrical potential V is given by the following equation.

V(x, y, z) = 5x2 − 2xy + xyz

(a) Find the rate of change of the potential at P(4, 6, 4) 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?

Math   Calculus   
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