Answer
$\sqrt{17}, \lt 4,1 \gt$
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 t^2 e^{st},e^{st}+ste^{st} \gt $
$\nabla f(0,2)=\lt 2^2 e^{0},e^{0}+s(0) \gt=\lt 4,1 \gt$
$|\nabla f(0,2)|=\sqrt{4^2+ 1^2}=\sqrt{17}$
Hence, the required answers are:
$\sqrt{17}, \lt 4,1 \gt$
