# The cost of fuel to propel a boat through water (in dollars per hour) is proportional to the cube...

## Question:

The cost of fuel to propel a boat through water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses $100 worth of fuel per hour when cruising at 10 mph. Apart from fuel, the cost of running the ferry (labor, etc.) is$675 per hour. At what speed should it travel so as to minimize the cost per mile traveled?

## Optimizing via Critical Points:

To find candidates for the maximum or minimum of a function, we can find the zeros of its derivative and evaluate them to see what the function values are at those points. This technique is especially useful when we have a cost function that we want to minimize.

Since the cost of fuel to propel a boat through water (in dollars per hour) is proportional to the cube of the speed, the fuel cost per hour can be...

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