Answer:
(x, f(x)) ≈ (5.5, 4)
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).