(62)

To find the smoothest solution to equation (6), we find the value of x that minimizes

.9 Here, ? is a constant that we introduce to make ? ) and

comparable quantities. Then

(Note here that ? is a scalar.) Expand the first term on the r.h.s. of this equation:

Then take the derivative of ?2 with respect to and set the result equal to 0 (using the method of §14.2):

We can rearrange this to get

This equation is satisfled if