# The energy required by a fish swimming at speed v to travel a distance

1. Jan 19, 2012

### girlygirl93

The energy required by a fish swimming at speed v to travel a distance L>0 in a current of speed u>0 is given by

E(v) = aL((v^3)/(v-u)), v>u

where a>0 is a proportionality constant.
a) Find the speed of the fish which results in minimal energy expenditure.
b) Give a qualitative sketch of the energy as a function of the speed of the fish.

I know that I am supposed to isolate v from the equation by using another equation in order to differentiate it, but I don't know how to. As well as a is a constant, and all values are positive. Also when I am drawing the sketch will the value a still be included? How do I include this in a graph?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Jan 19, 2012
2. Jan 19, 2012

### hotvette

Re: Optimizing

Why? If you want to minimize the function E(v) you need to differentiate E with respect to v and find out where it is zero.