Determine the direction in which f has maximum rate of increase from P. f(x, y, z) = xyz, P = (1, -2,9) (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) direction of maximum rate of increase: Determine the rate of change in that direction. (Give an exact answer. Use symbolic notation and fractions where needed.) rate of change: