anonymous
  • anonymous
i need a bit of clarification on why d/dx is always <0 to a given equation will type it out in the thread. anyone help me?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
dx/dt= rx(1-(x/k))-h < 0 if h>rk/4
anonymous
  • anonymous
i need to get my head around why this is
goformit100
  • goformit100
use the concept of maxima minin=ma...

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anonymous
  • anonymous
it what way? also how would this be derived?
anonymous
  • anonymous
Because i'm answering a question on logistic growth with harvesting, have found steady states by setting rx(1-(x/k))-h=0 giving a quadratic.
anonymous
  • anonymous
i need to find a critical harvesting point, which i have read is h_c=rk/4, and i need to be able to derive it.
TuringTest
  • TuringTest
can you tell me your original function, and what each variable represents please?
anonymous
  • anonymous
i will attach a print screen of the question i think that would explain what everything is.
anonymous
  • anonymous
@TuringTest i have attached the question.
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anonymous
  • anonymous
so for one solving rx(1-(x/k))-h=0 gives a quadratic, which gives the steady states. what i want to know, is, i have read that the critical value is h_c=rk/4 but how?
anonymous
  • anonymous
@TuringTest My assumption is maybe setting the discriminant of the quadratic to zero and rearranging. This does give h_c=rk/4. But i need to know that if this is correct why when h>h_c=rk/4 dx/dt is always 0.
TuringTest
  • TuringTest
hm... still thinking

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