Please answer all parts of the question. Show all of your work and explain each step with details. Thank you!

6. Given function f(r,y) = 3x y + 2ry', vector u = 4i - 3j, and point P(2, -1, -8) (a) Find the gradient Vf(r, y) (b) Evaluate the gradient at point P, i.e. find Vf (2, -1) (c) Find the rate of change of f at point P in the direction of vector u. (d) Find the direction (unit vector) in which f(x, y, 2) has maximum rate of change at point P. Also find the maximum rate of change. (e) Find the direction (unit vector) in which f(2, y, 2) has minimum rate of change at point P. Also find the minimum rate of change