It is suspected that the high amounts of tannin in mature oak leave inhibit the growth of the winter moth (Operophtera bromata L., Geometridae) larvae that extensively damage these trees in certain years. The following table lists the average weight of two samples of larvae at times in the first 28 days after birth. The first sample was reared on young oak leaves, whereas the second sample was reared on mature leaves from the same tree.
a. Use a natural cubic spline to approximate the average weight curve for each sample.
b. Find an approximate maximum average weight for each sample by determining the maximum of the spline.

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0 60 13 1720 28 Day Sample 1 average weight (m6.67 17.33 42.67 37.33 30.10 29.31 28.74 Sample 2 average weight (mg) 6.67 6.1 18.89 15.00 10.56 9448.89