Hi, please can you help me solve this question from i to v. 1. Dose Responsive Curve (Curve Sketching Problem) A dose response curve in pharmacology is a plot of the effectiveness R, of a drug as a...

1. Dose Responsive Curve (Curve Sketching Problem)

A dose response curve in pharmacology is a plot of the effectiveness R, of a drug as a function of the drug concentration c, such curves typically increase with an “S-shape” behaviour. A simple mathematical model of a dose response curve is given by the following equation:

R(c)=c²/3+c²

(a) Sketch the above graph for c ≥ 0 by following the steps below: i. Find the horizontal asymptotes, if any.

ii. Find the intervals of increase or decrease.
iii. Find the local maximum and minimum values.
iv. Find the intervals of concavity and the inflection point(s).

v. Use the information of parts (i)-(iv) to sketch the graph.

(b) Describe (in english) the behaviour of the responsive dose curve as the concentration of the drug increases.