Chapter 6.1, Problem 47E

EXERCISES

Dentin Growth The growth of dentin in the molars of mice has been studied by researchers in Copenhagen. They determined that the growth curve that best fits dentinal formation for the second molar is

$M(t)=-0.5035295+0.0229883t+0.0108021t^2-0.0003139t^3+0.0000025t^4,6\le t\le 48,$

Where $t$ is the age of the mouse (in days) and $M(t)$ is the cumulative dentin volume (in ${10}^{-1}m{m}^3$). Source: Journal of Craniofacial Genetics and Developmental Biology.

a. Use a graphing calculator to sketch the graph of this function on $[6,51]$ by $[0,4.5].$

b. Find the time at which the dentin formation is growing most rapidly. (Hint: Find the maximum value of the derivative of this function.