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(adsbygoogle = window.adsbygoogle || []).push({});

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

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

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