Let f(x,y,z) = x 2 y−xy 2 +z 3 , P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum and minimum directional derivative at P and give a vector along which this value is attained. I...

Let f(x,y,z) = x² y−xy²+z³, P(1,1,2),u is the vector from P to
Q(1, −2, −2). Determine the maximum and minimum directional derivative at P and
give a vector along which this value is attained.

I know that the max is sqrt(146) and the min is -[sqrt(146)].