Mathematics - Continuity - Differentiability Question with Solution | TestHub

Put $u=\sqrt{x-1}$. Near $x=1.5$, the radicals equal $\sqrt{(u-2{)}^2}=2-u$ and $\sqrt{(u-3{)}^2}=3-u$. Hence $f(x)=5-2u$ and $f\prime (1.5)=-1/\sqrt{0.5}=-\sqrt{2}$.