Consider the following function.

f$(4)=16,$ f$\text{'}(4)=8\mathrm{.}8$; x $=4\mathrm{.}5$

$($a$)$ Write a linearization for f with respect to x$.$

fL$($x$)=$

$($b$)$ Use the linearization to estimate f at the given input.

fL$(4\mathrm{.}5)=$