(1 point) Find the maximum rate of change of f(x, y) = ln(x + 12) at...

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(1 point) Find the maximum rate of change of f(x, y) = ln(x + 12) at the point (2, 3) and the direction in which it occurs. Maximum rate of change: sqrt52/13 Direction (unit vector) in which it occurs: ( 4/13 6/13 > (1 point) Suppose that f(x, y, z) = x yz xyz is a function of three variables. 1. Find the gradient of f(x, y, z). Answer: Vf(x, y, z) = i + 1/e(j) + 3k 2. Evaluate the gradient at the point P(2, -2, -1). Answer: Vf(2, -2, -1) = 88/5 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = Answer: D (2,-2, -1) = (6,-2,-32) (0, 1, 3 ) . (1 point) Find the maximum rate of change of f(x, y) = ln(x + 12) at the point (2, 3) and the direction in which it occurs. Maximum rate of change: sqrt52/13 Direction (unit vector) in which it occurs: ( 4/13 6/13 > (1 point) Suppose that f(x, y, z) = x yz xyz is a function of three variables. 1. Find the gradient of f(x, y, z). Answer: Vf(x, y, z) = i + 1/e(j) + 3k 2. Evaluate the gradient at the point P(2, -2, -1). Answer: Vf(2, -2, -1) = 88/5 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = Answer: D (2,-2, -1) = (6,-2,-32) (0, 1, 3 ) .