Answer
$f(x)=\frac{1}{4}x+1$
Work Step by Step
To establish a linearization, you must first find $f(a)$ and $f'(a)$ and make it into the following form $f(x)=f(a)+f'(a)\times(x-a) $ .
a = $4$ in this particular case.
$f'(a)$ = $\frac{1}{2\times\sqrt x}$ or 0.25
$f(a)$ = $\sqrt 4$ or 2
Thus:
$f(x) = 2+\frac{1}{4}\times (x-4)=\frac{1}{4}x+1$
