(1 point) Find the maximum rate of change of f(s, t) = test at the point...

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(1 point) Find the maximum rate of change of f(s, t) = test at the point (0,5). Answer: (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) = <2xyz-yz^3,x^2(z)-xz^3,x^2(y)-3xyz 2. Evaluate the gradient at the point P(2, 1, 2). Answer: Vf(-2, 1,-2) = 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = Answer: Du f(-2, 1, -2) = (0, 1, 3). (1 point) Find the maximum rate of change of f(s, t) = test at the point (0,5). Answer: (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) = <2xyz-yz^3,x^2(z)-xz^3,x^2(y)-3xyz 2. Evaluate the gradient at the point P(2, 1, 2). Answer: Vf(-2, 1,-2) = 3. Find the rate of change of f(x, y, z) at P in the direction of the vector u = Answer: Du f(-2, 1, -2) = (0, 1, 3).