Answer
$1, \lt \dfrac{3}{7},\dfrac{6}{7},\dfrac{-2}{7} \gt$
Work Step by Step
Formula to calculate the maximum rate of change of $f$: $D_uf=|\nabla f(x,y)|$
$\nabla f(x,y)=\lt \dfrac{1}{2}(\dfrac{1}{\sqrt{x^2+y^2+z^2})} (2x,2y,2z) \gt$
$\nabla f(3,6,-2)=\lt(\dfrac{1}{\sqrt{3^2+6^2+(-2)^2})} (3,6,-2) \gt=\lt \dfrac{3}{7},\dfrac{6}{7},\dfrac{-2}{7} \gt$
$|\nabla f(0,1)|=\sqrt{(\dfrac{3}{7})^2+(\dfrac{6}{7})^2+(\dfrac{-2}{7})^2}=1$
Hence, the required answers are:
$1, \lt \dfrac{3}{7},\dfrac{6}{7},\dfrac{-2}{7} \gt$
