Answer the following questions about the function f(x, y, z) = ln(x²z+y). (a) What is the directional derivative of f at the point (1, 1, 0) in the direction of the unit vector = (1, 0, ²)? (b) If you were at the point (1,1,0) and wanted to move in the direction in which the function f increases most quickly, what unit vector gives the direction you would go? (c) Let F= Vƒ be the gradient vector field of the function f and let C be the straight line segment from (0, 1, 4) to (1,0, e). What is the value of the line integral F dr? . u=

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