(1 point) Find the maximum rate of change of f(x, y) = ln(x + 12) at the point (3, -1) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs: ( (1 point) - Find the directional derivative of f(x, y, z) = z xy at the point (-1, 5, -2) in the direction of the vector v = (5, 5, 1). (1 point) Find the maximum rate of change of f(s, t) = test at the point (0, -3). Answer: (1 point) The temperature at a point (x, y, z) is given by T(x, y, z) = 1400e-x-2y-z where T is measured in C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -2, 2) in the direction toward the point Q(3, 4, 3). Answer: D f(2, 2, 2) = PQ 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer: