(1 point) Find the directional derivative of f(x, y, z) = 4y2 3x2 222 at the point P = (5, 1, 5) in the direction of the origin. (1 point) Find the maximum rate of change of f (x, y, z) = x + I at the point (3, 1, 3) and the direction in which it occurs. 2 Maximum rate of change: Direction in which it occurs: ) (1 point) Consider the function f (x, y) = (3x2 + yz). Find the the directional derivative of f at the point (2, 2) in the direction given by the angle 6 = 2 37f. Find the vector which describes the direction in which f is increasing most rapidly at (2, 2). (1 point) Suppose f(x, y) = i , P = (2, 3) and v = 1i+ 2j. )7 1. Find the gradient of f. Vf(x, y) = i+ .i 2. Find the gradient of f at the point P. V f (P) = i+ .i 3. Find the directional derivative of f at P in the direction of v. Duf(P) = 4. Find the maximum rate of change of f at P. 5. Find the (unit) direction vector in which the maximum rate of change occurs at P. i+ j