Exercise 1 (Anton, Rorres, p.676)

The density of water is known to reach a maximum at a temperature slightly above freezing. The following data is from the CRC Handbook of Chemistry and Physics and gives the density if water in gm/cm^3 for 5 temperatures (C).

T -10 0 10 20 30
D .99815 .99987 .99973 .99823 .99567

1. Find a cubic spline curve for the values.
2. Which interval contains the maximum? (Actually, this is obvious, but plot the spline anyway to verify.)
3. Find the equation of the spline on that interval, and use the usual calculus stuff to estimate where the density is maximized and what the maximum density is. The relevant calculus command is
Solve[D[functionname[x],x]==0], where you supply the function name.

In[122]:=

  values={{-10,.99815},{0,.99987},{10,.99973},{20,.99823},{30,.99567}}

Up to Interpolation and Splines (Curve Fitting)