Let f$($x$)=\frac{1}{\sqrt[\phantom{2}]{2x}}$

$.$

$($a$)(10$ points$)$ Use a second degree Taylor polynomial for $f(x)$

to estimate $(\frac{1}{\sqrt[\phantom{2}]{16\mathrm{.}1}})$

$($b$)(5$ points$)$ Use the Lagrange Error Bound formula to find an upper bound for the difference between the actual value of $(\frac{1}{\sqrt[\phantom{2}]{16}})$

and your estimate from part $($a$).$

$($c$)(5$ points$)$ Use a calculator to give a precise value of the error in your estimate from part $($a$).$ How does this answer compare with your answer from $($b$)$