Consider the following.

$f(x,y)=3x-5y$

$($a$)$ Find $f(10,4)$ and $f(10\mathrm{.}1,4\mathrm{.}05)$ and calculate $z.$

$f(10,4)=$

$f(10\mathrm{.}1,4\mathrm{.}05)=$

$z=$

$($b$)$ Use the total differential $dz$ to approximate $z.$

$dz=$

$$