Mathematics, 19.07.2019 21:00 gunnatvinson

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. it is believed that migrating fish try to minimize the total energy required to swim a fixed distance. if the fish are swimming against a current u (u < v), then the time required to swim a distance l is l / (v − u) and the total energy e required to swim the distance is given by e(v) = av3 · l v − u where a is the proportionality constant. (a) determine the value of v that minimizes e. note: this result has been verified experimentally.

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