Consider the function f(x, y, z) = xy + y² +². (a) What is the gradient grad f of f, and what is its value at the point (2,1,1)? (b) What is the rate of change of f at the point (2,1,1) in the direction of the unit vector = 1+4? (e) What is the maximum rate of change of f at the point (2,1,1), and in what direction does this maximum value occur?

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