For a fish swimming at a speed v relative to the water, the
energy expenditure per unit time is proportional to . 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
where a is the proportionality constant.
Determine the value of v that minimizes E. (Your answer may
depend on L, u and a).