Discuss the below:
Q: For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3. 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 less than 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)=av^3(L/[v-u])
where a is the proportionality constant.
(a)Determine the value of v that minimizes E.
(b)Sketch the graph of E.