here is the method they utilized w/o all the mumbo-jumbo ... hopefully you can follow what is going on.Find the points on the curve y = x^2 nearest to the point (0, 1).

distance between the two points and is

if one minimizes , then it also minimizes the square root of that value.

let

set ...

three critical values ... ,

use the 2nd derivative test ...

makes

is the location of a relative max

both make

both of these x-values minimize z

so, two points are the closest to (because of the symmetry of )

and