Question

A power station and a factory are on opposite sides of a river 50 feet wide. A power line must be run from the station to the factory. It costs 25 dollars per foot to run the cable in the river and $15 per foot on land. Express the total cost as a function of x, where x represents the distance downstream from the power station to the point where the cable touches land.

Answer 1

assume the line goes on the same side L, the n crosses.

cost=15L+25sqrt(50^2+(L-x)^2 )
Where L is the distance downstream to the factory.
So what is dcost/dx ?

check my thinking.

Answer 2

i have a similar question but instead of 50 its 60 aqnd 15 is 20