Let f(x,y,z) = x3z yz2. (a) If we start at the point (1,3,2), then in what direction should we move if we want to maximize the directional derivative? (b) What is the instantaneous rate of change of f if we change the variables in the direction from part (a)?

(c) What must be true for any direction if the instantaneous rate of change from (1,3,2) is equal to 0? What shape is formed by the collection of these vectors? (Be as specific as you can.)