A gradient field $is$ a function that assigns $to$ each point $in$ the domain $of$ a function $f,$ the

gradient vector gradf $at$ that point. The pictures below show the $(normalized)$ gradient fields

$of$ four different functions. Which gradient field corresponds $to$ which function? Explain.

$f_1(x,y)=-x^2-y^2,f_2(x,y)=xy$

$f_3(x,y)=x^2-y^2,f_4(x,y)=x-y$

$A$

$B$

$D$