Hello, I am a freshman in college at Western MI, I know how to use derivatives to find the minimum and maximum critical values of a function, but I am having a very hard time solving the following problem:
Borrowed from Calculus by Hughes-Hallett, et. al.
"The cost of fuel to propel a boat through the water, in dollars per hour, is proportional to the cube of the speed. A certain ferry uses $200 worth of fuel per hour when cruising at 10 miles per hour. Apart from fuel, the cost of running this ferry is $1050 per hour. At what speed should the ferry travel to minimize the cost per mile traveled?"
So far I have figured the following:
Cost (relative to speed) = 1/5s^3
and therefore:
Cost (per hour) = 1/5s^3 + 1050
I am having a hard time manipulating this equation to give me cost per mile traveled. Please help me!