Biomedical: “Efishency” At what speed should a fish swim upstream so as to reach its des...

Biomedical: “Efishency” At what speed should a fish swim upstream so as to reach its destination with the least expenditure of energy? The energy depends on the friction of the fish through the water and on the duration of the trip. If the fish swims with velocity v, the energy has been found experimentally to be proportional to v^k (for constant k > 2) times the duration of the trip. A distance of s miles against a current of speed c requires time (distance divided by speed).

The energy required is then proportional to .

For k = 3, minimizing energy is equivalent to minimizing

Find the speed v with which the fish should swim in order to minimize its expenditure E(v). (Your answer will depend on c, the speed of the current.)