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).