I need help on understanding what the question is asking.
A fish swims at a speed v relative to the water, against a current of 9 mi/h. Using a mathematical model of energy expenditure, it can be shown that the total energy E required to swim a distance of 18 mi is given by
E(v) = 2.73v^3(18/v ā 9)
.
Biologists believe that migrating fish try to minimize the total energy required to swim a fixed distance.
Find the value of v that minimizes energy required.

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- anonymous

- jamiebookeater

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- jim_thompson5910

You'll need to find the derivative E ' (v) first

- jim_thompson5910

were you able to find it? or no?

- anonymous

yes it is
(98.28v^3ā1326.78v^2)/(vā9)^2

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## More answers

- jim_thompson5910

I'm guessing the original function is this?\[\Large E(v) = 2.73v^3\left(\frac{18}{v-9}\right)\]I forgot to ask
If it is, then you have the correct derivative

- anonymous

Yes thank you I solved for v and received the right answer

- jim_thompson5910

you should get v = 13.5

- Jaynator495

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