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

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(1 point) Find the maximum rate of change of f(x, y) = ln(x + y) 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 Entered Answer Preview Result Message i+0.367879j+3k i + j + 3k incorrect e 17.6 (6,-2,-32) 88 85 incorrect Your answer isn't a vector (it looks like a real number) Your answer isn't a number (6,-2,-32) incorrect (it looks like a point) At least one of the answers above is NOT correct. (1 point) Suppose that f(x, y, z) = xyz - 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 = (0,-). Answer: Du f(2, -2, -1) = (6,-2,-32) Message Your answer isn't a vector incorrect (it looks like a real number) Entered Answer Preview Result 17.6 85 88 The answer above is NOT correct. (1 point) Find the gradient of the function f(x, y, z) = z In(xy), at the point (1, e, -1) Vf(1, e, -1) = 88/5 (1 point) Find the maximum rate of change of f(x, y) = ln(x + y) 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 Entered Answer Preview Result Message i+0.367879j+3k i + j + 3k incorrect e 17.6 (6,-2,-32) 88 85 incorrect Your answer isn't a vector (it looks like a real number) Your answer isn't a number (6,-2,-32) incorrect (it looks like a point) At least one of the answers above is NOT correct. (1 point) Suppose that f(x, y, z) = xyz - 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 = (0,-). Answer: Du f(2, -2, -1) = (6,-2,-32) Message Your answer isn't a vector incorrect (it looks like a real number) Entered Answer Preview Result 17.6 85 88 The answer above is NOT correct. (1 point) Find the gradient of the function f(x, y, z) = z In(xy), at the point (1, e, -1) Vf(1, e, -1) = 88/5