This is a Mathematica file to solve Problem 68, p. 309.
Note the funny way that functions are defined: using the underscore.
![[Graphics:Images/5.3_gr_1.gif]](Images/5.3_gr_1.gif)
![[Graphics:Images/5.3_gr_3.gif]](Images/5.3_gr_3.gif)
![[Graphics:Images/5.3_gr_5.gif]](Images/5.3_gr_5.gif)
![[Graphics:Images/5.3_gr_8.gif]](Images/5.3_gr_8.gif)
But since -2 is less than zero, it's not in the domain (time must be positive). Only 2 hours is an interesting potential critical point.
![[Graphics:Images/5.3_gr_10.gif]](Images/5.3_gr_10.gif)
This is less than zero, so we have a relative max. That's good!
![[Graphics:Images/5.3_gr_12.gif]](Images/5.3_gr_12.gif)
So 3/4% is the maximum concentration.
![[Graphics:Images/5.3_gr_14.gif]](Images/5.3_gr_14.gif)
Yep! Sure enough, a maximum.