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How to find the direction of maximum/minimum rate of change?

I know how to calculate the rate of change at a point in a direction but can't find anything to help me answer this question asking me for the direction of maximum/minimum rate of change (for a multivariable function).
Would help to see the question, but direction of maximum change is parallel to grad f (i.e. ∇f\nabla f) and minimum change is anything perpendicular to that.
Find the rate of change of f(x, y, z) = x^3+(y^2)*z at the point x0 = (2, 1, 1) with respect to the
change of position of the unit vector u in the direction of the vector (1, 3, 1). Hence, calculate the
directional derivative Duf(2, 1, 1). In which (unit) directions do the maximum and minimum rates
of change occur?

(it's the last part I can't answer but this is the entire question)
Then my answer above applies.

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