Consider the function. f(x, y) = 3 x 3 y 2 (a) Sketch the graph of f in the first octant and plot the point (3, 2, 1) on the surface. (Select the correct graph.) (b) Find Duf(3, 2), where u = cos(????)i + sin(????)j, using each given value of ????. (i) ???? = ???? 4 (ii) ???? = 2???? 3 (iii) ???? = 4???? 3 (iv) ???? = ???? 6 (c) Find Duf(3, 2), where u = v v , using each given vector v. (i) v = i + j (ii) v = 3i 4j (iii) v is the vector from (1, 2) to (2, 6) (iv) v is the vector from (3, 2) to (4, 5) (d) Find f(x, y). f(x, y) = (e) Find the maximum value of the directional derivative at (3, 2). (f) Find a unit vector u orthogonal to f(3, 2) and calculate Duf(3, 2). Duf(3, 2) = Discuss the geometric meaning of the result. f is the direction of ---Select--- rate of change of f. So, in a direction orthogonal to f, the rate of change of f is