Answer Happy

Consider the general logistic function, P(x)=1+Ae−kxM​, with A,M, and k all positive. Calculate P′(x) and P′′(x). (Express numbers in exact form. Use symbolic notation and fractions where needed.) P′(x)= p′′(x)= Find any horizontal asymptotes of P (Give your answer as a comma-separated list of values. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNR if no such asymptotes exist.) horizontal asymptote(s) at P=
Identify intervals where P is increasing and decreasing. (For any interval, give your answer as an interval in the form (**). Use the symbol ∞ for infinity, ∪ for combining intervals, and an appropriate type of parentheses "( (.")","[ ", or "]" depending on whether the interval is open or closed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if no such interval exists.) P is increasing on: P is decreasing on: Calculate any inflection points of P. (Give your answer as a comma-separated list of points in the form (∗∗ ). Express numbers in exact form. Use symbolic notation and fractions where needed.)