\(\fbox{1}\) Logistic (non-calculator)
Let \[f(x) = \frac{a}{b+e^{-kx}}\]
[This is called a logistic function]
(i) Find the two horizontal asympotes
(ii) Then show that the rate of change of \(f(x)\) is greatest midway between these two asymptotes.
[This is called a logistic function]
(i) Find the two horizontal asympotes
(ii) Then show that the rate of change of \(f(x)\) is greatest midway between these two asymptotes.