1. Consider function g(x, y, 2) = z In(a² + y³). (a) Find the gradient vector of g at P(-1,1,2). (b) Find the directional derivative of g(x, y, z) = z In(x² + y³) at P in the direction of i =< 1,1, –1>. (c) Find the direction at which g has the maximum rate of change of g at P. What is the maximum rate?

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