## TedG 2 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?

1. TedG

dx/dt= rx(1-(x/k))-h < 0 if h>rk/4

2. TedG

i need to get my head around why this is

3. goformit100

use the concept of maxima minin=ma...

4. TedG

it what way? also how would this be derived?

5. TedG

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

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

can you tell me your original function, and what each variable represents please?

8. TedG

i will attach a print screen of the question i think that would explain what everything is.

9. TedG

@TuringTest i have attached the question.

10. TedG

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

@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

hm... still thinking