What is the point of maximum growth rate? round to the nearest tenth.

  (x, f(x)) ≈ (5.5, 4)

Step-by-step explanation:

You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...

  4 = 8/(1 +3e^(-0.2x))

  1 +3e^(-0.2x) = 8/4 = 2

  e^(-0.2x) = 1/3

  x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5

We already know the value of f(x) is 4 there.

The point of maximum growth is about (5.5, 4).

good luck on your studies! : )

david edward.