You are told that there $is$ a function $f$ whose partial derivatives are $f_x(x,y)=5y+x$ and $f_y(x,y)=5x-y.$

One way $to$ verify this claim $isto$ integrate $f_x$ and $f_y$ with respect $tox$ and $y$ respectively:

$(a)(i)$ Integrate $f_x$ with respect $tox$ and call the antiderivative $f_1(x,y).$ You can keep $or$ ignore the constant $of$ integration $in$ your answer.

$f_1(x,y)=$

$(a)(ii)$ Integrate $f_y$ with respect $toy$ and call the antiderivative $f_2(x,y).$ You can keep $or$ ignore the constant $of$ integration $in$ your answer.

$f_2(x,y)=$

$(b)$ Now, compare del$\frac{f_1}{d}$ely with $f_y$ and del$\frac{f_2}{d}$elx with $f_x.Isit$ possible for $fto$ exist?

False

$(c)Is$ there $an$ easier way $of$ verifying whether such $anf$ exists?

Yes there $is$; simply compare the derivative $of{f}_{x}w.r.ty$ and that $of$

$No,$ the process above $is$ the only way.

Yes there $is$; provided that $we$ are given two points $of$ the function $f$

True

$(Clearmy$ choice$)$