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TedG

  • 3 years ago

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?

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  1. TedG
    • 3 years ago
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    dx/dt= rx(1-(x/k))-h < 0 if h>rk/4

  2. TedG
    • 3 years ago
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    i need to get my head around why this is

  3. goformit100
    • 3 years ago
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    use the concept of maxima minin=ma...

  4. TedG
    • 3 years ago
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    it what way? also how would this be derived?

  5. TedG
    • 3 years ago
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    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.

  6. TedG
    • 3 years ago
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    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.

  7. TuringTest
    • 3 years ago
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    can you tell me your original function, and what each variable represents please?

  8. TedG
    • 3 years ago
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    i will attach a print screen of the question i think that would explain what everything is.

  9. TedG
    • 3 years ago
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    @TuringTest i have attached the question.

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  10. TedG
    • 3 years ago
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    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?

  11. TedG
    • 3 years ago
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    @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.

  12. TuringTest
    • 3 years ago
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    hm... still thinking

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