Tutorial Exercise

Determine whether $or$ not $Fis$ a conservative vector field. $Ifitis,$ find a function $f$ such that $F=f.$

$F(x,y)=(2x-7y)i+(-7x+8y-8)j$

Step $1$

Recall that a vector field

$F(x,y)=P(x,y)i+Q(x,y)j$

$is$ conservative $if$

$Qx$

$=$

$$

$y$

$.$