Suppose that 0 < y 0 < N. Let b = (N - y 0 )/y 0

Question:

Suppose that 0 < y₀ < N. Let b = (N - y₀)/y₀ , and let y(x) = N/(1 + be^-kx) for all x. Show the following.
(a) 0 < y(x) < N for all x.
(b) The lines y = 0 and y = N are horizontal asymptotes of the graph.
(c) y(x) is an increasing function.
(d) ((ln b)/k, N/2) is a point of inflection of the graph.
(e) dy/dx is a maximum at x0 = (ln b)/k.