a population is modeled by the logistic differntial equation dP/dt= (P/3)(1-(P/8)). if P(0)=2, for what value of P is the population growing the fastest?

Question

anonymous · Answer

When p=8 population growth is highest because equating above to 0 we get 0 and 8 and on substituting this results in second derivative we get -ve value for it when p=8 and +ve value for p=0.
According to definition max value exists for -ve value of the second derivative and so the answer is 8

anonymous · Answer

Did u got it or u need me to explain again????

anonymous · Answer

That's what i put, but the book says that the answer is 4...

anonymous · Answer

Then the answer in the book is wrong as this is clearly crystal correct

anonymous · Answer

But when i put the answer 4 in the equation, the value of dP/dt was higher than when i plugged in 8 (which gives you 0).

anonymous · Answer

what is the actual equation?????

anonymous · Answer

they never gave that

anonymous · Answer

If we integrate the given equation and substitute,then we will get 96/27 for p=8 and 48/27 for p=4 which gives max value for 8.. Once check it....

anonymous · Answer

ok thanks