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.

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

E(v)=av^3*(L)/(v-u)

E(v)=aLv^3/(v-u)

(v-u)*(3aLv^2)-(aLv^3)

E'(v)=___________________________

(v-u)^2

2*au^3*L-3av^2 *u^2

0=________________________

v^2-2vu+u^2

v=3u/2

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