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Given the function, f(x, y, z) - x y + x\\33 + z. a. In which direction does f(T, y, 2) increase most rapidly at P( - 2, 1, 3). Write your answer in component form. Direction is b. Find the maximum rate of increase at P( = 2, 1, 3). Maximum Rate of Increase is c. Compute the directional derivative of f (x, y, z) at P( - 2, 1, 3) in the direction of i | 4j + 3k. Derivative is