Maximum rate of change?

Question

How would I calculate the maximum rate of change of f at the point (1,-2,-3) and the direction that it occurs of the function:

f(x,y,z)=ln(x*(y^2)*(z^3))

First person with correct answer and work gets 10 pts!

Answer 1

grad f(x,y,z) = (1/x, 2/y, 3/z)
grad f(1,-2,-3) = (1,-1,-1)
Ι grad f(1,-2,-3) Ι = √3
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