Constrained critical points

Still better approximations to P(a) are available by our general method. Simply using the same quadrature rule separately on [O, r/8] and [v/8, r/4] and adding the results should divide the error by about 64, since for multistep applications the error formula shows the error is O(h6). Of course, that requires evaluating t(0) at five points instead of three, but f'(0) is still evaluated only at 0 = O and r/4. If we are willing to evaluate f(0) at five or more points, we can also use a quadrature rule of higher order. But Q(a) already gives all the accuracy ever needed for elementary statistics classes.