Suppose that over a certain region of space the electrical potential v is given by the following equation. v(x, y, z) = 2x2 − 5xy + xyz (a) find the rate of change of the potential at p(2, 6, 7) 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?