Mathematics, 21.03.2020 08:18 angie07253
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 the formula below, where a is the proportionality constant.
E(v) = av^3 L/(v - u)
Determine the value of v that minimizes E. (Note: This result has been verified experimentally.)
Answers: 2
that minimize E.
, where a is a proportionality constant.
![aL\frac{d}{dv}[\frac{v^{3}}{v - u} ] = 0](/tpl/images/0557/5182/025d3.png)
![aL[\frac{3v^{2}(v - u) - v^{3} }{(v - u)^{2} } ] = 0](/tpl/images/0557/5182/e30b4.png)
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