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## anonymous one year ago 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 − 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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1. jim_thompson5910

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

2. jim_thompson5910

were you able to find it? or no?

3. anonymous

yes it is (98.28v^3−1326.78v^2)/(v−9)^2

4. 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

5. anonymous

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

6. jim_thompson5910

you should get v = 13.5

7. Jaynator495

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