Dose-Response of Multi-Vitamins Multi-vitamins typically have dose-response curves of the following form R = f(x) = (ax) /( k^2 + x^2) , x ≥ 0, where x is a measure of the daily dose, R is a measure of the health benefits, and a and k are positive constants.

(e) Is there a dosage that maximizes the health benefits? If so, find the dosage, and find the maximum health benefit.

(f) Is there a dosage that minimizes the health benefits? If so, find the dosage, and find the minimum health benefit.

(g) Graph the function using the information from the previous parts and interpret your graph in terms of the health benefits of the multi-vitamins.