Thread: Minimizing Cost

An offshore oil well is 2 km off the coast. The refinery is 4 km down the coast. Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost? How is the distance found exactly?

Distance (C)=2√(4+x^2 )+(4-x)
Dc/Dx=2(1/2)(√(4+x^2 ))(2x)+ (4-x)