Answer
$\dfrac{\sqrt {17}}{2}, \lt 0,\dfrac{1}{2},2 \gt$
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 \ln (yz)y , x/y,x/z \gt $
$\nabla f(1,2,\dfrac{1}{2})=\lt \ln 1, 1/2,2 \gt=\lt 0,\dfrac{1}{2},2 \gt$
$|\nabla f(1,2,\dfrac{1}{2})|=\sqrt{0^2+(\dfrac{1}{2})^2+2^2}=\dfrac{\sqrt {17}}{2}$
Hence, the required answers are:
$\dfrac{\sqrt {17}}{2}, \lt 0,\dfrac{1}{2},2 \gt$
