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.

Question

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.

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

were you able to find it? or no?

anonymous · Answer

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

jim_thompson5910 · Answer

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 · Answer

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

jim_thompson5910 · Answer

you should get v = 13.5

jaynator495 · Answer

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