Maxima and Minima

The reaction R of the body to a dose D of a certain drug is such that R=D^{2}\left(\displaystyle \frac{1}{2}C-\displaystyle \frac{1}{3}D\right) for 0\leqD\leqC.  Sketch the graph of R as a function of D.  If the sensitivity is the rate of change of R and D, find for what value of D is the sensitivity is a maximum.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 2: Question 12, p. 11)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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