Derivate solution?

[Guest]

Hello,
If anyone can help me, I appreciate

tks

how to solve this problem? If you can write the solution , ... tks



problem

A bird is foraging for berries. If it stays too long in any one patch it will be spending valuable foraging time looking for the hidden berries, but when it leaves it will have to spend time finding another patch. A model for the net amount of food energy in joules the bird gets if it spends t minutes in a patch is E = 3000 t / (t+4) . Suppose the bird takes 2 min on average to find each new patch, and spends negligible energy doing so. How long should the bird spend in a patch to maximize its average rate of energy gain over the time spent flying to a patch and foraging in it?

[shyamjayakannan]

Since the time spent searching for patches is constant, we only need to maximize the rate of energy gain while the bird is in a patch. Noe, rate of energy gain = [tex]\frac{dE}{dt}[/tex]. So, to maximize this, we differentiate it further and equate it to 0 to find the maxima.

So, you need to solve [tex]\frac{d^2E}{dt^2}=0[/tex]