Answer
$10.025$
Work Step by Step
$f(x)$ = $x^{\frac{1}{2}}$
$f'(x)$ = $\frac{1}{2\sqrt x}$
$f'(x)$ = $\frac{f(x+h)-f(x)}{h}$
$x$ = $100$, $h$ = $0.5$
$f'(100)$ = $\frac{f(100.5)-f(100)}{0.5}$
$\frac{1}{2\sqrt {100}}$ = $\frac{f(100.5)-\sqrt {100}}{0.5}$
$f(100.5)$ = $10.025$
