Team 15
Casey Sweetser
Glenn Radliff
David Yeh
34. 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<v) and the total energy E required to swim the distance is given by

where a is the proportionality constant.

a) Determine the value of v that minimizes E.
b) Sketch the graph of E.

Note:   This result has been verified experimentally;  migrating fish swim against a current at a speed 50% greater than the current speed.

       2*au^3*L-3av^2 *u^2


graph of E(v)                 since a is a constant, we set to one.  L is a constant so we set to 1.