Answer
All the points on the line $y=x+1 $
Work Step by Step
Formula to calculate the maximum rate of change of $f$: $D_uf=|\nabla f(x,y)|$
$\nabla f(x,y)=\lt 2x-2,2y-4 \gt$
Direction vector: $\lt 1,1 \gt$
Thus, $\lt 2x-2,2y-4 \gt=n\lt 1,1 \gt$
This implies
$n=2x-2, n=2y-4$ and $2x-2=2y-4$
Hence, the required answer is:
All the points on the line $y=x+1 $
