Question: Question 1. Given a scalar function f(x, y, z) = x2 - xev + y2z2. a) Find the directional derivative of f(x, y, z) at

Question 1. Given a scalar function f(x, y, z) = x2 - xev + y2z2. a) Find the directional derivative of f(x, y, z) at (1,0,1) in the direction y = 21 + 31 - k. (4 marks) b) Find the direction in which the function f(x, y,z) is increasing most rapidly at the same point (1,0,1) (4 marks) C) If now given a surface f (x, y,z) = 0, find the direction of the normal to the plane at (1,0,1), as well as the equation to the tangent plane at the same point (1,0,1) (7 marks)

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