$(10$ points$)$ Use a $2^{nd}$ degree Taylor polynomial for $f(x)=\sqrt[\phantom{2}]{x}$ to approximate $\sqrt[\phantom{2}]{1\mathrm{.}2}.$

$($Hints: Choose a center close to $1\mathrm{.}2$ and remember $\sqrt[\phantom{2}]{x}=x^{\frac{1}{2}})$

$F(x)=\sqrt[\phantom{2}]{1\mathrm{.}2}=1\mathrm{.}08s$