A graphing calculator is recommended.

A fish swims at a speedvrelative to the water, against a current of9mi/h. Using a mathematical model of energy expenditure, it can be shown that the total energyErequired to swim a distance of18miis given byE(v) = 2.73v³

18

v9

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Biologists believe that migrating fish try to minimize the total energy required to swim a fixed distance. Find the value ofvthat minimizes energy required.

[Note:This result has been verified; migrating fish swim against a current at a speed 50% greater than the speed of the current.]

v=