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Growth of population/Logistic differential equation/Example/Properties of solution curves/Exercise

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Consider the solutions

to the logistic differential equation we have found in an example.

a) Sketch up the graph of this function (for suitable and ).

b) Determine the limits for and .

c) Study the monotony behavior of these functions.

d) For which does the derivative of have a maximum (For the function itself, this represents an inflection point).