Given f(x, y, z) = x²y + y²z+ z²x and P(1,−1, 1), do the following. (a) Find (i) the direction of maximum increase and (ii) the maximum increase at P. (b) Find (i) the direction of maximum decrease and (ii) the maximum decrease at P. (c) Find the tangent plane of directions where the directional derivative is zero at P.