Mathematics - Application of Derivative Question with Solution | TestHub

A factory is 5 km from a straight railway at the perpendicular foot $B$. Town $A$ lies on the railway with $AB=\lambda \mathrm{km}$. A connection point $P$ lies on $AB$ with $AP=x$. Highway freight costs twice railway freight, so, up to a common factor, total cost is $F(x)=x+2\sqrt{25+(\lambda -x{)}^2}$ for $0\le x\le \lambda$. If $\lambda =185/\sqrt{3}\mathrm{km}$, which $x$ minimizes the charge?